The document describes hypothesis testing to resolve a conflict between a drug company and doctor over a snoring drug. It involves:
1) The null hypothesis is that the drug cures 90% of people, based on the company's claim. The alternative is that it cures less than 90%.
2) A test on 15 patients found 11 were cured. This is lower than expected if the null was true.
3) Hypothesis testing is used to determine if there is strong evidence against the null. It finds the results are not significant enough to reject the null hypothesis and the drug company's claims.
Statistical inference involves using probability concepts to draw conclusions about populations based on samples. It includes point and range estimation to estimate population values, as well as hypothesis testing to test hypotheses about populations. Hypothesis testing involves making a null hypothesis and an alternative hypothesis before collecting sample data. Common hypotheses include claims of no difference or significant differences. Statistical tests like z-tests, t-tests, and chi-square tests are used to either accept or reject the null hypothesis based on the sample data and a significance level, typically 5%. P-values indicate the probability of observing the sample results by chance. Type 1 and type 2 errors can occur when making inferences about hypotheses.
This document provides an introduction to hypothesis testing and summarizes key concepts such as the null and alternative hypotheses, outcome measures, effect sizes, confidence intervals, statistical significance, and p-values. It explains how to state the research question, assumptions, and hypotheses. It also outlines the steps to choosing a statistical test, calculating test statistics, and forming conclusions based on p-values and significance levels. Various effect sizes are defined, including risk ratio, risk difference, and odds ratio. Interpretation of confidence intervals and limitations of significance testing are also briefly covered.
Hypothesis testing involves 4 steps: 1) stating the null and alternative hypotheses, 2) setting the significance level criteria, 3) computing a test statistic to evaluate the hypotheses, and 4) making a decision to either reject or fail to reject the null hypothesis based on the significance level and test statistic. The goal is to correctly identify true null hypotheses while minimizing errors like falsely rejecting a true null hypothesis (Type I error) or retaining a false null hypothesis (Type II error).
This document discusses hypothesis testing, which is a method used in scientific research to either accept or reject hypotheses. It outlines the key steps:
1) Formulating a research question and hypothesis, which is either the null hypothesis or alternative hypothesis. The null hypothesis is the statement being tested.
2) Collecting and analyzing data and using a statistical test to calculate the p-value, which represents the probability of obtaining results as extreme as the actual outcome by chance alone.
3) Comparing the p-value to a predetermined significance level (usually 5%) to either reject or fail to reject the null hypothesis, with lower p-values leading to rejection. This determines whether the results support the alternative hypothesis.
Hypothesis testing involves making an assumption about an unknown population parameter, called the null hypothesis (H0). A hypothesis is tested by collecting a sample from the population and comparing sample statistics to the hypothesized parameter value. If the sample value differs significantly from the hypothesized value based on a predetermined significance level, then the null hypothesis is rejected. There are two types of errors that can occur - type 1 errors occur when a true null hypothesis is rejected, and type 2 errors occur when a false null hypothesis is not rejected. Hypothesis tests can be one-tailed, testing if the sample value is greater than or less than the hypothesized value, or two-tailed, testing if the sample value is significantly different from the hypothesized value.
Okay, let me try to analyze this step-by-step:
1) Null Hypothesis (H0): The advertisement had no effect on sales.
2) Alternative Hypothesis (H1): The advertisement increased sales.
3) We can test this using a paired t-test, since we have sales data from the same shops before and after.
4) Calculate the mean difference between before and after sales for each shop. Then take the average of those differences.
5) Use the t-statistic to determine if the average difference is significantly greater than 0, which would indicate the advertisement increased sales.
So in summary, a paired t-test can be used to determine if the advertisement
Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
Statistical inference involves using probability concepts to draw conclusions about populations based on samples. It includes point and range estimation to estimate population values, as well as hypothesis testing to test hypotheses about populations. Hypothesis testing involves making a null hypothesis and an alternative hypothesis before collecting sample data. Common hypotheses include claims of no difference or significant differences. Statistical tests like z-tests, t-tests, and chi-square tests are used to either accept or reject the null hypothesis based on the sample data and a significance level, typically 5%. P-values indicate the probability of observing the sample results by chance. Type 1 and type 2 errors can occur when making inferences about hypotheses.
This document provides an introduction to hypothesis testing and summarizes key concepts such as the null and alternative hypotheses, outcome measures, effect sizes, confidence intervals, statistical significance, and p-values. It explains how to state the research question, assumptions, and hypotheses. It also outlines the steps to choosing a statistical test, calculating test statistics, and forming conclusions based on p-values and significance levels. Various effect sizes are defined, including risk ratio, risk difference, and odds ratio. Interpretation of confidence intervals and limitations of significance testing are also briefly covered.
Hypothesis testing involves 4 steps: 1) stating the null and alternative hypotheses, 2) setting the significance level criteria, 3) computing a test statistic to evaluate the hypotheses, and 4) making a decision to either reject or fail to reject the null hypothesis based on the significance level and test statistic. The goal is to correctly identify true null hypotheses while minimizing errors like falsely rejecting a true null hypothesis (Type I error) or retaining a false null hypothesis (Type II error).
This document discusses hypothesis testing, which is a method used in scientific research to either accept or reject hypotheses. It outlines the key steps:
1) Formulating a research question and hypothesis, which is either the null hypothesis or alternative hypothesis. The null hypothesis is the statement being tested.
2) Collecting and analyzing data and using a statistical test to calculate the p-value, which represents the probability of obtaining results as extreme as the actual outcome by chance alone.
3) Comparing the p-value to a predetermined significance level (usually 5%) to either reject or fail to reject the null hypothesis, with lower p-values leading to rejection. This determines whether the results support the alternative hypothesis.
Hypothesis testing involves making an assumption about an unknown population parameter, called the null hypothesis (H0). A hypothesis is tested by collecting a sample from the population and comparing sample statistics to the hypothesized parameter value. If the sample value differs significantly from the hypothesized value based on a predetermined significance level, then the null hypothesis is rejected. There are two types of errors that can occur - type 1 errors occur when a true null hypothesis is rejected, and type 2 errors occur when a false null hypothesis is not rejected. Hypothesis tests can be one-tailed, testing if the sample value is greater than or less than the hypothesized value, or two-tailed, testing if the sample value is significantly different from the hypothesized value.
Okay, let me try to analyze this step-by-step:
1) Null Hypothesis (H0): The advertisement had no effect on sales.
2) Alternative Hypothesis (H1): The advertisement increased sales.
3) We can test this using a paired t-test, since we have sales data from the same shops before and after.
4) Calculate the mean difference between before and after sales for each shop. Then take the average of those differences.
5) Use the t-statistic to determine if the average difference is significantly greater than 0, which would indicate the advertisement increased sales.
So in summary, a paired t-test can be used to determine if the advertisement
Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
This document discusses statistical significance and p-values. It explains that statistical significance determines whether differences in experimental and control groups are real or due to chance. Tests of significance are used to measure the influence of chance, and results are considered statistically significant if p < 0.05, meaning there is less than a 5% probability the results are due to chance. The document provides examples of interpreting p-values in experiments.
This document provides an introduction to hypothesis testing. It discusses the components of a hypothesis test, including the null and alternative hypotheses, types of errors, and controlling errors. Specifically, it explains that the null hypothesis is the statement being tested, while the alternative is what would be true if the null is false. Type I error is rejecting the null when it is true, while Type II error is failing to reject a false null. The significance level and power help control these errors.
This document discusses hypothesis testing and p-values. It begins by defining a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are formulated and tested through science to evaluate their credibility. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a rival relationship. Hypothesis testing uses sample data to evaluate whether differences observed could be due to chance (the null hypothesis) or are real effects (the alternative hypothesis). Key concepts discussed include type 1 and type 2 errors, significance levels, one-sided and two-sided tests, and the relationship between p-values, confidence intervals, and the strength of evidence against
This document discusses hypothesis testing and p-values. It defines a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are tested to evaluate their credibility against observed data. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a relationship different from the null. Errors in hypothesis testing can occur if the decision to reject or fail to reject the null hypothesis is wrong. The p-value indicates how likely the observed or more extreme results would be if the null hypothesis were true. A lower p-value provides stronger evidence against the null hypothesis.
Lecture6 Applied Econometrics and Economic Modelingstone55
The manager of a pizza restaurant conducted an experiment to determine if customers prefer a new baking method for pepperoni pizzas. He provided 100 randomly selected customers with both an old-style and new-style pizza and had them rate the difference on a scale from -10 to 10. Based on the customer ratings, the manager wants to use hypothesis testing to determine if he should switch to the new baking method. The null hypothesis is that customers are indifferent between the methods, while the alternative hypothesis is that customers prefer the new method. The results of the experiment provide strong statistical evidence to reject the null hypothesis and support switching to the new baking method.
This document discusses hypotheses, hypothesis testing, and research bias. It defines a hypothesis as a tentative assumption about a population parameter that is statistically tested. The main types of hypotheses covered are the null hypothesis (H0), which is attempted to be disproven, and the alternative hypothesis (H1). The four steps of hypothesis testing are outlined as stating the hypotheses, collecting sample data, calculating sample statistics, and analyzing results to accept or reject H0. Key concepts discussed include p-values, levels of significance, type I and type II errors, and bias. Common biases explained are selection, memory/recall, confounding, and interviewer bias.
- Hypothesis testing involves testing assumptions about population parameters by analyzing sample data. The goal is to either accept or reject the null hypothesis based on the sample evidence.
- There are two hypotheses - the null hypothesis, which assumes no effect or relationship between variables, and the alternative hypothesis, which assumes an effect or relationship.
- The procedure involves setting the null hypothesis, collecting sample data, and using a statistical test to determine whether to reject or accept the null hypothesis based on the level of difference between the sample and null hypothesis. If the difference is significant, the null is rejected.
This document introduces hypothesis testing, which determines whether a treatment has an effect. It discusses how a sample is taken, a treatment is administered, and the sample is measured. Hypothesis testing decides if any difference is due to the treatment or just sampling error. The null hypothesis states there is no effect, while alternatives consider if the difference is too large to be due to chance. Tests compute a statistic, compare it to a critical value, and either reject or fail to reject the null hypothesis. Type I and II errors are possible. Effect size measures are also important to consider alongside significance.
This document summarizes key concepts in statistical analysis and inference as they relate to neuroimaging data. It discusses signal detection theory, types of errors in statistical tests, vocabulary used, and how statistical values are converted to p-values. It then covers various methods for multiple comparisons correction including Bonferroni correction, permutation testing, and false discovery rate correction. Cluster-based analysis and random field theory are also summarized. The document notes some limitations of p-values and advocates for effect sizes, replicability, and sharing of full results.
1. The document introduces hypothesis testing using the example of testing claims made by a cornflakes salesman about the amount of cornflakes in each box.
2. It describes how to formulate the null and alternative hypotheses, choose a significance level, determine the appropriate test statistic, calculate critical values, compare the test statistic to the critical values, and state a conclusion.
3. It provides three examples of testing the salesman's claims when he is thought to be conservative, a cheat, or clueless. It walks through applying the hypothesis testing steps to each example.
This document discusses key concepts related to sampling, including:
- The population is the total group of interest, while the study population is the subset that participates.
- Probability and non-probability sampling methods are described. Probability methods allow estimation of sampling error.
- Important factors for sample representativeness are the sampling procedure, sample size, and participant response rate.
- Formulas are provided for calculating sample sizes needed for single or two group estimates, proportions, and comparing means while controlling type 1 error and achieving desired statistical power.
The document provides an introduction to hypothesis testing, including its real-life applications, key definitions, and structure. It defines hypothesis testing as the process of testing the validity of a statistical hypothesis based on a random sample from a population. The document outlines the common steps in hypothesis testing: 1) stating the null and alternative hypotheses, 2) choosing a significance level, 3) determining the test statistic and decision criteria, 4) rejecting or failing to reject the null hypothesis, and 5) drawing a conclusion. It also defines important terminology like population mean, null and alternative hypotheses, test statistic, significance level, critical region, and p-value. Real-life examples from pharmaceutical testing and legal cases are provided to illustrate the motivation for hypothesis
This document discusses hypothesis testing and outlines the five-step procedure:
1) State the null and alternative hypotheses
2) Select the level of significance
3) Identify the appropriate test statistic
4) Formulate the decision rule
5) Make a decision about whether to reject the null hypothesis
Examples are provided to illustrate one-tailed and two-tailed hypothesis tests using z-tests when the population standard deviation is known. Critical value and decision rule approaches are demonstrated.
(1) Hypothesis testing involves stating a null hypothesis and alternative hypothesis about characteristics of a population.
(2) Key steps include collecting data, specifying assumptions, defining hypotheses, calculating a test statistic, determining its distribution, setting a decision rule, and making a statistical conclusion.
(3) The null hypothesis is tested by calculating a test statistic and comparing it to rejection regions based on the statistic's distribution to determine whether to reject or fail to reject the null hypothesis.
This document provides an overview of key concepts related to the normal distribution, sampling distributions, estimation, and hypothesis testing. It defines important terms like the normal curve, z-scores, sampling distributions, point and interval estimates, and the steps of hypothesis testing including stating hypotheses, collecting data, and determining whether to reject the null hypothesis. It also reviews concepts like the central limit theorem, standard error, bias, confidence intervals, types of errors in hypothesis testing, and factors that influence test statistics.
The document defines key concepts in hypothesis testing such as critical value, significance level, p-value, type I and type II errors, and power. It states that the critical value divides the normal distribution into regions for rejecting or failing to reject the null hypothesis. The significance level corresponds to the critical region. A p-value less than 0.05 indicates the result is statistically significant. Type I error occurs when the null hypothesis is rejected when it is true, while type II error is failing to reject a false null hypothesis. Power is defined as 1 - β, where β is the probability of a type II error.
This presentation discusses the following topics:
Hypothesis Test
Potential Outcomes in Hypothesis Testing
Significance level
P-value
Sampling Errors
Type I Error
What causes Type I errors?
What causes Type II errors?
4 possible outcomes
A hypothesis is a prediction about the outcome of an experiment. Hypothesis testing uses sample data to evaluate the credibility of a hypothesis. The null hypothesis predicts that the independent variable will have no effect on the dependent variable, while the alternative hypothesis predicts it will have an effect. Researchers conduct statistical tests to either reject or fail to reject the null hypothesis based on whether the sample data is consistent with it.
Hypothesis testing is an important tool in research. A hypothesis is a statement or proposition that can be tested through scientific investigation. The null hypothesis represents the default position that there is no relationship between variables or no difference among groups. The alternative hypothesis is what the researcher aims to prove. Through hypothesis testing, researchers aim to reject the null hypothesis by collecting data and calculating the probability of the results if the null hypothesis were true. This probability is then compared to the pre-determined significance level, often 5%, to determine whether to reject or fail to reject the null hypothesis. Proper hypothesis testing involves clearly stating the hypotheses, selecting a random sample, determining the appropriate statistical test based on the data, and interpreting the results.
The document discusses the steps involved in testing a null hypothesis. It outlines the key steps as stating the null and alternative hypotheses, choosing an appropriate statistical test, specifying the significance level and sample size, choosing a sampling distribution and critical region, and deciding whether to accept or reject the null hypothesis. It also provides an example where the null hypothesis is that a new flu drug is no more effective than the standard treatment, with the alternative being that the new drug is more effective.
This document discusses drug testing and the use of Bayes' theorem to determine the probability that an individual testing positive for a drug actually uses the drug. It provides an example where a drug test is 99% sensitive and specific, and 0.5% of the population uses the drug. Even with the accurate test, if an individual tests positive it is more likely they do not use the drug due to the small number of actual drug users compared to the large number of non-users, resulting in more false positives than true positives. The surprising conclusion is that out of all positive tests, only about 33% would actually be users, with the rest being false positives.
This document discusses statistical significance and p-values. It explains that statistical significance determines whether differences in experimental and control groups are real or due to chance. Tests of significance are used to measure the influence of chance, and results are considered statistically significant if p < 0.05, meaning there is less than a 5% probability the results are due to chance. The document provides examples of interpreting p-values in experiments.
This document provides an introduction to hypothesis testing. It discusses the components of a hypothesis test, including the null and alternative hypotheses, types of errors, and controlling errors. Specifically, it explains that the null hypothesis is the statement being tested, while the alternative is what would be true if the null is false. Type I error is rejecting the null when it is true, while Type II error is failing to reject a false null. The significance level and power help control these errors.
This document discusses hypothesis testing and p-values. It begins by defining a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are formulated and tested through science to evaluate their credibility. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a rival relationship. Hypothesis testing uses sample data to evaluate whether differences observed could be due to chance (the null hypothesis) or are real effects (the alternative hypothesis). Key concepts discussed include type 1 and type 2 errors, significance levels, one-sided and two-sided tests, and the relationship between p-values, confidence intervals, and the strength of evidence against
This document discusses hypothesis testing and p-values. It defines a hypothesis as a proposition or prediction about the outcome of an experiment. Hypotheses are tested to evaluate their credibility against observed data. There are two main types of hypotheses: the null hypothesis, which corresponds to a default or general position, and the alternative hypothesis, which asserts a relationship different from the null. Errors in hypothesis testing can occur if the decision to reject or fail to reject the null hypothesis is wrong. The p-value indicates how likely the observed or more extreme results would be if the null hypothesis were true. A lower p-value provides stronger evidence against the null hypothesis.
Lecture6 Applied Econometrics and Economic Modelingstone55
The manager of a pizza restaurant conducted an experiment to determine if customers prefer a new baking method for pepperoni pizzas. He provided 100 randomly selected customers with both an old-style and new-style pizza and had them rate the difference on a scale from -10 to 10. Based on the customer ratings, the manager wants to use hypothesis testing to determine if he should switch to the new baking method. The null hypothesis is that customers are indifferent between the methods, while the alternative hypothesis is that customers prefer the new method. The results of the experiment provide strong statistical evidence to reject the null hypothesis and support switching to the new baking method.
This document discusses hypotheses, hypothesis testing, and research bias. It defines a hypothesis as a tentative assumption about a population parameter that is statistically tested. The main types of hypotheses covered are the null hypothesis (H0), which is attempted to be disproven, and the alternative hypothesis (H1). The four steps of hypothesis testing are outlined as stating the hypotheses, collecting sample data, calculating sample statistics, and analyzing results to accept or reject H0. Key concepts discussed include p-values, levels of significance, type I and type II errors, and bias. Common biases explained are selection, memory/recall, confounding, and interviewer bias.
- Hypothesis testing involves testing assumptions about population parameters by analyzing sample data. The goal is to either accept or reject the null hypothesis based on the sample evidence.
- There are two hypotheses - the null hypothesis, which assumes no effect or relationship between variables, and the alternative hypothesis, which assumes an effect or relationship.
- The procedure involves setting the null hypothesis, collecting sample data, and using a statistical test to determine whether to reject or accept the null hypothesis based on the level of difference between the sample and null hypothesis. If the difference is significant, the null is rejected.
This document introduces hypothesis testing, which determines whether a treatment has an effect. It discusses how a sample is taken, a treatment is administered, and the sample is measured. Hypothesis testing decides if any difference is due to the treatment or just sampling error. The null hypothesis states there is no effect, while alternatives consider if the difference is too large to be due to chance. Tests compute a statistic, compare it to a critical value, and either reject or fail to reject the null hypothesis. Type I and II errors are possible. Effect size measures are also important to consider alongside significance.
This document summarizes key concepts in statistical analysis and inference as they relate to neuroimaging data. It discusses signal detection theory, types of errors in statistical tests, vocabulary used, and how statistical values are converted to p-values. It then covers various methods for multiple comparisons correction including Bonferroni correction, permutation testing, and false discovery rate correction. Cluster-based analysis and random field theory are also summarized. The document notes some limitations of p-values and advocates for effect sizes, replicability, and sharing of full results.
1. The document introduces hypothesis testing using the example of testing claims made by a cornflakes salesman about the amount of cornflakes in each box.
2. It describes how to formulate the null and alternative hypotheses, choose a significance level, determine the appropriate test statistic, calculate critical values, compare the test statistic to the critical values, and state a conclusion.
3. It provides three examples of testing the salesman's claims when he is thought to be conservative, a cheat, or clueless. It walks through applying the hypothesis testing steps to each example.
This document discusses key concepts related to sampling, including:
- The population is the total group of interest, while the study population is the subset that participates.
- Probability and non-probability sampling methods are described. Probability methods allow estimation of sampling error.
- Important factors for sample representativeness are the sampling procedure, sample size, and participant response rate.
- Formulas are provided for calculating sample sizes needed for single or two group estimates, proportions, and comparing means while controlling type 1 error and achieving desired statistical power.
The document provides an introduction to hypothesis testing, including its real-life applications, key definitions, and structure. It defines hypothesis testing as the process of testing the validity of a statistical hypothesis based on a random sample from a population. The document outlines the common steps in hypothesis testing: 1) stating the null and alternative hypotheses, 2) choosing a significance level, 3) determining the test statistic and decision criteria, 4) rejecting or failing to reject the null hypothesis, and 5) drawing a conclusion. It also defines important terminology like population mean, null and alternative hypotheses, test statistic, significance level, critical region, and p-value. Real-life examples from pharmaceutical testing and legal cases are provided to illustrate the motivation for hypothesis
This document discusses hypothesis testing and outlines the five-step procedure:
1) State the null and alternative hypotheses
2) Select the level of significance
3) Identify the appropriate test statistic
4) Formulate the decision rule
5) Make a decision about whether to reject the null hypothesis
Examples are provided to illustrate one-tailed and two-tailed hypothesis tests using z-tests when the population standard deviation is known. Critical value and decision rule approaches are demonstrated.
(1) Hypothesis testing involves stating a null hypothesis and alternative hypothesis about characteristics of a population.
(2) Key steps include collecting data, specifying assumptions, defining hypotheses, calculating a test statistic, determining its distribution, setting a decision rule, and making a statistical conclusion.
(3) The null hypothesis is tested by calculating a test statistic and comparing it to rejection regions based on the statistic's distribution to determine whether to reject or fail to reject the null hypothesis.
This document provides an overview of key concepts related to the normal distribution, sampling distributions, estimation, and hypothesis testing. It defines important terms like the normal curve, z-scores, sampling distributions, point and interval estimates, and the steps of hypothesis testing including stating hypotheses, collecting data, and determining whether to reject the null hypothesis. It also reviews concepts like the central limit theorem, standard error, bias, confidence intervals, types of errors in hypothesis testing, and factors that influence test statistics.
The document defines key concepts in hypothesis testing such as critical value, significance level, p-value, type I and type II errors, and power. It states that the critical value divides the normal distribution into regions for rejecting or failing to reject the null hypothesis. The significance level corresponds to the critical region. A p-value less than 0.05 indicates the result is statistically significant. Type I error occurs when the null hypothesis is rejected when it is true, while type II error is failing to reject a false null hypothesis. Power is defined as 1 - β, where β is the probability of a type II error.
This presentation discusses the following topics:
Hypothesis Test
Potential Outcomes in Hypothesis Testing
Significance level
P-value
Sampling Errors
Type I Error
What causes Type I errors?
What causes Type II errors?
4 possible outcomes
A hypothesis is a prediction about the outcome of an experiment. Hypothesis testing uses sample data to evaluate the credibility of a hypothesis. The null hypothesis predicts that the independent variable will have no effect on the dependent variable, while the alternative hypothesis predicts it will have an effect. Researchers conduct statistical tests to either reject or fail to reject the null hypothesis based on whether the sample data is consistent with it.
Hypothesis testing is an important tool in research. A hypothesis is a statement or proposition that can be tested through scientific investigation. The null hypothesis represents the default position that there is no relationship between variables or no difference among groups. The alternative hypothesis is what the researcher aims to prove. Through hypothesis testing, researchers aim to reject the null hypothesis by collecting data and calculating the probability of the results if the null hypothesis were true. This probability is then compared to the pre-determined significance level, often 5%, to determine whether to reject or fail to reject the null hypothesis. Proper hypothesis testing involves clearly stating the hypotheses, selecting a random sample, determining the appropriate statistical test based on the data, and interpreting the results.
The document discusses the steps involved in testing a null hypothesis. It outlines the key steps as stating the null and alternative hypotheses, choosing an appropriate statistical test, specifying the significance level and sample size, choosing a sampling distribution and critical region, and deciding whether to accept or reject the null hypothesis. It also provides an example where the null hypothesis is that a new flu drug is no more effective than the standard treatment, with the alternative being that the new drug is more effective.
This document discusses drug testing and the use of Bayes' theorem to determine the probability that an individual testing positive for a drug actually uses the drug. It provides an example where a drug test is 99% sensitive and specific, and 0.5% of the population uses the drug. Even with the accurate test, if an individual tests positive it is more likely they do not use the drug due to the small number of actual drug users compared to the large number of non-users, resulting in more false positives than true positives. The surprising conclusion is that out of all positive tests, only about 33% would actually be users, with the rest being false positives.
This document provides an overview of key concepts in inferential statistics including parameter estimation, hypothesis testing, t-tests, linear regression, and analysis of variance (ANOVA). It defines important statistical terms like population parameter, point estimate, confidence interval, null and alternative hypotheses, type I and II errors, and significance. Common statistical tests covered include the one sample t-test, independent two sample t-test, and tests assumptions. Linear regression models and correlation are also discussed including the regression line, coefficient of correlation, and coefficient of determination.
The document discusses key concepts related to research methodology and hypothesis testing. It defines the following:
- Null and alternative hypotheses, with the null hypothesis representing what is being tested and the alternative representing other possibilities.
- Type I and Type II errors in hypothesis testing, with Type I being rejection of a true null hypothesis and Type II being acceptance of a false null hypothesis.
- Significance levels which determine the probability of a Type I error, with common values being 0.10, 0.05, and 0.01.
- Power which is the probability of correctly rejecting a false null hypothesis and can be increased by raising the significance level, increasing sample size, or considering alternatives further from the null.
Testing of Hypothesis combined with tests.pdfRamBk5
This document discusses hypothesis testing procedures. It defines a hypothesis as a statement about a population parameter that can be tested. The key points covered are:
- Null and alternative hypotheses are defined, with the null hypothesis containing "=", "<", or ">" and the alternative containing "≠", "<", or ">"
- Tests can be one-tailed or two-tailed depending on the alternative hypothesis
- The level of significance and critical values are used to determine whether to reject or fail to reject the null hypothesis
- Type I and type II errors are explained as incorrect rejections or failures to reject the null hypothesis
- Parametric and non-parametric tests are compared based on their data
WHAT IS PROBABILITYInsight into the use of probability .docxalanfhall8953
WHAT IS PROBABILITY?
Insight into the use of probability in the medical community:
Probability is a recurring theme in medical practice. No doctor who returns home from a busy day at the hospital is spared the nagging feeling that some of his diagnoses may turn out to be wrong, or some of his treatments may not lead to the expected cure. Encountering the unexpected is an occupational hazard in clinical practice. Doctors after some experience in their profession reconcile to the fact that diagnosis and prognosis always have varying degrees of uncertainty and at best can be stated as probable in a particular case.
Critical appraisal of medical journals also leads to the same gut feeling. One is bombarded with new research results, but experience dictates that well-established facts of today may be refuted in some other scientific publication in the following weeks or months. When a practicing clinician reads that some new treatment is superior to the conventional one, he will assess the evidence critically, and at best he will conclude that probably it is true.
Types of probabilities
Suppose that we want to determine the probability of obtaining an ace from a pack of cards (which, let us assume has been tampered with by a dishonest gambler), we proceed by drawing a card from the pack a large number of times, as we know in the long run, the observed frequency will approach the true probability. Since there are 4 aces in a 52 card deck, the real probably of drawing an ace on a single draw would be ¼ or 7.69%. Mathematicians often state that a probability is a long-run frequency. Consider the statement, “The cure for Alzheimer’s disease will probably be discovered in the coming decade.” This statement does not indicate the basis of this expectation or belief. However, it may be based on the present state of research in Alzheimer’s. A probabilistic statement incorporates some amount of uncertainty, which may be quantified as follows: A politician may state that there is a fifty-fifty chance of winning the next election.
Consider a 26-year-old married female patient who suffered from severe abdominal pain is referred to a hospital. She is also having amenorrhea for the past 4 months. The pain is located in the left lower abdomen. The gynecologist who examines her concludes that there is a 30% probability that the patient is suffering from ectopic pregnancy.
If you were to ask the gynecologist to explain on what basis the diagnosis of ectopic pregnancy is suspected, the Dr. might state that he/she has studied a large number of successive patients with this symptom complex of lower abdominal pain with amenorrhea, and that a subsequent laparotomy revealed an ectopic pregnancy in 30% of the cases.
If we accept that the study cited is large enough to make us assume that the possibility of the observed frequency of ectopic pregnancy, it is natural to conclude that the gynecologist’s probability claim is ‘evidence based’.
Medical False Positives a.
Example of a one-sample Z-test The previous lecture in P.docxcravennichole326
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a.
Example of a one-sample Z-test The previous lecture in P.docxelbanglis
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a ...
The four steps of hypothesis testing are:
1. State the null and alternative hypotheses. The null hypothesis assumes the claim is true while the alternative contradicts it.
2. Set the significance level, typically 5%, which is the probability of a Type I error of rejecting a true null hypothesis.
3. Compute the test statistic to determine how far the sample mean is from the population mean stated in the null hypothesis.
4. Make a decision by comparing the p-value to the significance level. If p < 0.05, reject the null hypothesis.
This document discusses hypothesis testing and key concepts related to testing hypotheses. It defines the null and alternative hypotheses, Type I and Type II errors, p-values, power, effect size, and sample size. Specifically, it explains that the null hypothesis assumes no difference or effect, while the alternative hypothesis proposes a difference or effect. It also defines a p-value as the probability of obtaining results as extreme as or more extreme than the actual results if the null hypothesis is true. A small p-value leads to rejecting the null hypothesis while a large p-value fails to reject it.
This document provides an overview of clinical trials and their various phases. It discusses how clinical trials are used to test potential interventions in humans to determine if they should be adopted for general use. The different phases of clinical trials are described, including phase I-IV. Key aspects of clinical trial design such as randomization, blinding, and placebos are explained. Hypothesis testing and its role in statistical analysis is also summarized.
Researchers use hypothesis testing to evaluate claims about populations by taking samples and comparing sample statistics to hypothesized population parameters. The four steps of hypothesis testing are:
1) State the null and alternative hypotheses, with the null hypothesis presuming the claim is true.
2) Set criteria for deciding whether to reject the null hypothesis.
3) Calculate a test statistic from the sample.
4) Compare the test statistic to the criteria to determine whether to reject the null hypothesis.
Researchers use hypothesis testing to evaluate claims about populations by taking samples and analyzing the results. The four steps of hypothesis testing are: 1) stating the null and alternative hypotheses, 2) setting the significance level typically at 5%, 3) computing a test statistic to quantify how unlikely the sample results would be if the null was true, and 4) making a decision to either reject or fail to reject the null hypothesis based on comparing the test statistic to the significance level. The goal is to systematically evaluate whether a hypothesized population parameter, such as a mean, is likely to be true based on the sample results.
Chapter8 introduction to hypothesis testingBOmebratu
Researchers use hypothesis testing to evaluate claims about populations by taking samples and comparing sample statistics to hypothesized population parameters. The four steps of hypothesis testing are:
1) State the null and alternative hypotheses, with the null hypothesis presuming the claim is true.
2) Set criteria for deciding whether to reject the null hypothesis.
3) Calculate a test statistic from the sample.
4) Compare the test statistic to the criteria to determine whether to reject the null hypothesis.
Researchers use hypothesis testing to evaluate claims about populations by taking samples and comparing sample statistics to hypothesized population parameters. The four steps of hypothesis testing are:
1) State the null and alternative hypotheses, with the null hypothesis presuming the claim is true.
2) Set criteria for deciding whether to reject or fail to reject the null hypothesis.
3) Calculate a test statistic from the sample.
4) Compare the test statistic to the criteria to either reject or fail to reject the null hypothesis.
- A researcher is evaluating whether a null hypothesis (H0: μ = 80) should be rejected using sample data. The combination of factors (sample mean (μ) and sample size (n)) that is most likely to result in rejecting the null hypothesis is μ = 10 and n = 50. With a larger sample size and mean further from the null hypothesized mean, this combination provides the highest chance of rejecting the null hypothesis.
- Hypothesis testing involves using sample data to evaluate hypotheses about population parameters. The researcher states hypotheses, collects data, and uses a test statistic to determine whether to reject or fail to reject the null hypothesis. Type I and II errors can occur.
- Key factors that influence the likelihood
P-values the gold measure of statistical validity are not as reliable as many...David Pratap
This is an article that appeared in the NATURE as News Feature dated 12-February-2014. This article was presented in the journal club at Oman Medical College , Bowshar Campus on December, 17, 2015. This article was presented by Pratap David , Biostatistics Lecturer.
Hypothesis testing is a statistical technique used to determine if a treatment has an effect on a population. It involves taking a sample from a population, administering a treatment, measuring the results, and then using a hypothesis test to evaluate if any differences are likely due to the treatment or just chance. The null hypothesis states there is no effect, and the alternative hypothesis states there is an effect. The test calculates a statistic and compares it to a critical value to either reject or fail to reject the null hypothesis. Errors can occur if the wrong conclusion is reached. [/SUMMARY]
The document discusses hypothesis testing, which involves testing a hypothesis about a population using a sample of data. It explains that a hypothesis test has four main steps: 1) stating the null and alternative hypotheses, where the null hypothesis asserts there is no difference between the sample and population, 2) setting the significance level, 3) determining the test statistic and critical region for rejecting the null hypothesis, and 4) making a decision to reject or fail to reject the null hypothesis based on whether the test statistic falls in the critical region. Type I and type II errors are also defined. The document provides examples of null and alternative hypotheses using mathematical symbols and discusses how to determine if a p-value is statistically significant.
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2. NOT EVERYTHING YOU’RE TOLD IS ABSOLUTELY CERTAIN
• The trouble is, how do you know when what you’re being told isn’t right? Hypothesis tests give
you a way of using samples to test whether or not statistical claims are likely to be true. They give
you a way of weighing the evidence and testing whether extreme results can be explained by
mere coincidence.
3. NEW SCENARIO
Statsville’s new miracle drug
• Statsville’s leading drug company has produced a new remedy for curing snoring. Frustrated snorers are
flocking to their doctors in hopes of finding nightly relief.
• The drug company claims that their miracle drug cures 90% of people within two weeks, which is great news
for the people with snoring difficulties. The trouble is, not everyone’s convinced
4. • The doctor at the Statsville Surgery has been prescribing SnoreCull to her patients, but she’s disappointed by
the results. She decides to conduct her own trial of the drug.
• She takes a random sample of 15 snorers and puts them on a course of SnoreCull for two weeks. After two
weeks, she calls them back in to see whether their snoring has stopped.
• Here are the results:
5. • If the drug cures 90% of people, how many people in the sample of 15 snorers would you expect to have
been cured? What sort of distribution do you think this follows?
6. • 90% of 15 is 13.5, so you’d expect 14 people to be cured. Only 11 people in the doctors sample were cured,
which is much lower than the result you’d expect
• There are a specific number of trials and the doctor is interested in the number of successes, so the
number of successes follows a binomial distribution. If X is the number of successes then X ~ B(15, 0.9).
7. SO WHAT’S THE PROBLEM?
• Here’s the probability distribution for how many people the drug company says should have been cured by the
snoring remedy.
• So why the discrepancy?
8. • The drug company might not be deliberately telling lies, but their claims might be misleading.
• It’s possible that the tests of the drug company were flawed, and this might have resulted in misleading claims
being made about SnoreCull. They may have inadvertent conducted flawed or biased tests on SnoreCull,
which resulted in them making inaccurate predictions about the population. If the success rate of SnoreCull is
actually lower than 90%, this would explain why only 11 people in the sample were cured.
9. The drug company’s claims might actually be accurate.
• Rather than the drug company being at fault, it’s always possible that the patients in the doctor’s sample may
not have been representative of the snoring population as a whole. It’s always possible that the snoring remedy
does cure 90% of snorers, but the doctor just happens to have a higher proportion of people in her sample
whom it doesn’t cure. In other words, her sample might be biased in some way, or it could just come down to
there being a small number of patients in the sample.
Resolving the conflict from 50,000 feet
• So how do we resolve the conflict between the doctor and the drug company? Let’s take a very high level view
of what we need to do. We can resolve the conflict between the drug company and the doctor byputting the
claims of the drug company on trial.
• In other words, we’ll accept the word of the drug company by default, but if there’s strong evidence against it,
we’ll side with the doctor instead.
11. • In general, this process is called hypothesis testing, as you take a hypothesis or claim and then test it against the
evidence. Let’s look at the general process for this.
12. THE SIX STEPS FOR HYPOTHESIS TESTING
• Here are the broad steps that are involved in hypothesis testing. We’ll go through each one in detail in the
following pages.
13. THE DRUG COMPANY’S CLAIM
• According to the drug company, SnoreCull cures 90% of patients within 2 weeks. We need to accept this
position unless there is sufficiently strong evidence to the contrary.
• The claim that we’re testing is called the null hypothesis. It’s represented by H0, and it’s the claim that we’ll
accept unless there is strong evidence against it.
14. SO WHAT’S THE NULL HYPOTHESIS FOR SNORECULL?
• The null hypothesis for SnoreCull is the claim of the drug company: that it cures 90% of patients. This is the
claim that we’re going to go along with, unless we find strong evidence against it.
• We need to test whether at least 90% of patients are cured by the drug, so this means that the null hypothesis is
that p = 90%.
So what’s the alternative?
• We’ve looked at what the claim is we’re going to test, the null hypothesis, but what if it’s not true? What’s the
alternative?
15. • The counterclaim to the null hypothesis is called the alternate hypothesis. It’s represented by H1, and it’s the
claim that we’ll accept if there’s strong enough evidence to reject H0.
• The doctor believes that SnoreCull cures less than 90% of people, so this means that the alternate hypothesis is
that p < 90%.
16. • When hypothesis testing, you assume the null hypothesis is true. If there’s sufficient evidence against it,
you reject it and accept the alternate hypothesis.
Step 2: Choose your test statistics
• Now that you’ve determined exactly what it is you’re going to test, you need some means of testing it. You can
do this with a test statistic. The test statistic is the statistic that you use to test your hypothesis. It’s the statistic
that’s most relevant to the test.
What’s the test statistic for SnoreCull?
• In our hypothesis test, we want to test whether SnoreCull cures 90% of people or more. To test this, we can
look at the probability distribution according to the drug company, and see whether the number of successes
in the sample is significant.
• If we use X to represent the number of people cured in the sample, this means that we can use X as our test
statistic. There are 15 people in the sample, and the probability of success according to the drug company is
0.9. As X follows a binomial distribution, this means that the test statistic is actually:
17. • We choose the test statistic according to H0, the null hypothesis.
• We need to test whether there is sufficient evidence against the null hypothesis, and we do this by first
assuming that H0 is true. We then look for evidence that contradicts H0. For the SnoreCull hypothesis test, we
assume that the probability of succes,s is 0.9 unless there is strong evidence against this being true.
• To do this, we look at how likely it is for us to get the results we did, assuming the probability of success is 0.9.
In other words, we take the results of the sample and examine the probability of getting that result.We do this
by finding a critical region.
18. STEP 3: DETERMINE THE CRITICAL REGION
• The critical region of a hypothesis test is the set of values that present the most extreme evidence against the
null hypothesis.
• Let’s see how this works by taking another look at the doctor’s sample. If 90% or more people had been
cured, this would have been in line with the claims made by the drug company. As the number of people
cured decreases, the more unlikely it becomes that the claims of the drug company are true.
• Here’s the probability distribution:
19. AT WHAT POINT CAN WE REJECT THE DRUG COMPANY CLAIMS?
• What we need is some way of indicating at what point we can reasonably reject the null hypothesis, and we can
do this by specifying a critical region. If the number of snorers cured falls within the critical region, then we’ll
say there is sufficient evidence to reject the null hypothesis. If the number of snorers cured falls outside the
critical region, then we’ll accept that there isn’t sufficient evidence to reject the null hypothesis, and we’ll accept
the claims of the drug company. We’ll call the cut off point for the critical region c, the critical value.
• So how do we choose the critical region?
20. TO FIND THE CRITICAL REGION, FIRST DECIDE ON THE SIGNIFICANCE LEVEL
• Before we can find the critical region of the hypothesis test, we first need to decide on the significance level.
The significance level of a test is a measure of how unlikely you want the results of the sample to be before you
reject the null hypothesis Ho. Just like the confidence level for a confidence interval, the significance level is
given as a percentage.
• As an example, suppose we want to test the claims of the drug company at a 5% level of significance. This
means that we choose the critical region so that the probability of fewer than c snorers being cured is less than
0.05. It’s the lowest 5% of the probability distribution.
21. • The significance level is normally represented by the Greek letter𝛼. The lower 𝛼 is, the more unlikely the
results in your sample need to be before we reject Ho.
So what significance level should we use?
• Let’s use a significance level of 5% in our hypothesis test. This means that if the number of snorers cured in
the sample in the lowest 5% of the probability distribution, then we will reject the claims of the drug company.
If the number of snorers cured lies in the top 95% of the probability distribution, then we’ll decide there isn’t
enough evidence to reject the null hypothesis, and accept the claims of the drug company. If we use X to
represent the number of snorers cured, then we define the critical region as being values such that
22. • When you’re constructing a critical region for your test, another thing you need to be aware of is whether
you’re conducting a one-tailed or two-tailed test. Let’s look at the difference between the two, and what impact
this has on the critical region?
• A one-tailed test is where the critical region falls at one end of the possible set of values in your test. You
choose the level of the test—represented by 𝛼—and then make sure that the critical region reflects this as a
corresponding probability.
• The tail can be at either end of the set of possible values, and the end you use depends on your alternate
hypothesis H1.
• If your alternate hypothesis includes a < sign, then use the lower tail, where the critical region is at the lower
end of the data.
• If your alternate hypothesis includes a > sign, then use the upper tail, where the critical region is at the upper
end of
• the data. We’re using a one-tailed test for the SnoreCull hypothesis test with the critical region in the lower tail,
as our alternate hypothesis is that p < 0.9.
23.
24. TWO-TAILED TESTS
• A two-tailed test is where the critical region is split over both ends of the set of values. You choose the level of
the test , and then make sure that the overall critical region reflects this as a corresponding probability by
splitting it into two. Both ends contain /2, so that the total is .
• You can tell if you need to use a two-tailed test by looking at the alternate hypothesis H1. If H1 contains a
sign, then you need to use a two-tailed test as you are looking for some change in the parameter, rather than an
increase or decrease.
• We would have used a two-tailed test for our SnoreCull if our alternate hypothesis had been p 0.9. We
would have had to check whether significantly more or significantly fewer than 90% of patients had been cured
25. FIND THE P-VALUE
• Now that we’ve looked at critical regions, we can move on to step 4, finding the p-value.
• A p-value is the probability of getting a value up to and including the one in your sample in the direction of
your critical region. It’s a way of taking your sample and working out whether the result falls within the critical
region for your hypothesis test. In other words, we use the p-value to say whether or not we can reject the null
hypothesis.
How do we find the p-value?
• How we find the p-value depends on our critical region and our test statistic. For the SnoreCull test, 11 people
were cured, and our critical region is the lower tail of the distribution. This means that our p-value is P(X 11),
where X is the distribution for the number of people cured in the sample.
• As the significance level of our test is 5%, this means that if P(X 11) is less than 0.05, then the value 11 falls
within the critical region, and we can reject the null hypothesis.
26. • We know from step 2 that X ~ B(15, 0.9). What’s P(X ≤ 11)?
27. • A p-value is the probability of getting the results in the sample, or something more extreme, in the
direction of the critical region.
• In our hypothesis test for SnoreCull, the critical region is the lower tail of the probability distribution. In order
to see whether 11 people being cured of snoring is in the critical region, we calculated P(X 11), as this is the
probability of getting a result at least as extreme as the results of our sample in the direction of the lower tail.
• Had our critical region been the upper tail of the probability distribution instead, we would have needed to
find P(X 11). We would have counted more extreme results as being greater than 11, as these would have
been closer to the critical region.
28. STEP 5: IS THE SAMPLE RESULT IN THE CRITICAL REGION?
• Now that we’ve found the p-value, we can use it to see whether the result from our sample falls within the
critical region. If it does, then we’ll have sufficient evidence to reject the claims of the drug company
• Our critical region is the lower tail of the probability distribution, and we’re using a significance level of 5%.
This means that we can reject the null hypothesis if our p-value is less that 0.05. As our p-value is 0.0555, this
means that the number of people cured by SnoreCull in the sample doesn’t fall within the critical region.
29. STEP 6: MAKE YOUR DECISION
• We’ve now reached the final step of the hypothesis test. We can decide whether to accept the null hypothesis,
or reject it in favor of the alternative.
• The p-value of the hypothesis test falls just outside the critical region of the test. This means that there isn’t
sufficient evidence to reject the null ,In other words:
We accept the claims of the drug company hypothesis.