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1. The document discusses the process of hypothesis testing, which involves stating a null hypothesis (H0) and an alternative hypothesis (H1), choosing a significance level, selecting a test statistic, and making a decision to reject or not reject the null hypothesis. 2. Key steps in hypothesis testing are identifying the problem, stating the hypotheses, choosing a significance level, selecting an appropriate test statistic, computing test statistics from sample data, and making a decision to reject or not reject the null hypothesis based on the critical region. 3. Errors in hypothesis testing include Type I errors of rejecting a true null hypothesis and Type II errors of not rejecting a false null hypothesis. The significance level determines the probability of a Type I
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The document discusses hypothesis testing, including the key concepts of the null and alternative hypotheses, types of errors, and approaches to testing hypotheses. It provides examples of hypothesis tests for a population mean. The null hypothesis is initially assumed to be true, and sample data are used to determine if there is sufficient evidence against the null in favor of the alternative hypothesis. The rejection region and p-value approaches are outlined as methods to evaluate the sample data relative to the critical values or significance level and determine whether to reject or fail to reject the null hypothesis.
Study unit 4 (oct 2014)
This document provides an overview of hypothesis testing methodology for one population. It defines key concepts like the null and alternative hypotheses, types of errors, test statistics, significance levels, and rejection regions. The two main approaches to hypothesis testing are presented: the rejection region approach and the p-value approach. Steps for conducting a hypothesis test are outlined, including stating hypotheses, choosing test criteria, collecting data, determining test statistics and p-values, and making conclusions. Examples are provided to illustrate hypothesis tests for means and proportions.
Study unit 4 (oct 2014)
This document provides an overview of hypothesis testing methodology for one population. It defines key concepts like the null and alternative hypotheses, types of errors, test statistics, significance levels, and rejection regions. The two main approaches to hypothesis testing are presented: the rejection region approach and the p-value approach. Steps for conducting a hypothesis test are outlined, including stating hypotheses, choosing test criteria, collecting data, determining test statistics and p-values, and making conclusions. Examples are provided to illustrate hypothesis tests for means and proportions.
Hypothesis_Testing.ppt
1) Hypothesis testing involves making an educated guess about a population parameter and designing a study to analyze sample data to determine if the population characteristic is likely or unlikely.
2) The null hypothesis states what is assumed to be true about the population parameter, while the alternative hypothesis is what would be accepted if the null is rejected. Type I and Type II errors occur when the wrong conclusion is reached.
3) Key aspects of hypothesis testing include defining the test statistic, rejection region, significance level, and whether a one-tailed or two-tailed test is appropriate based on the alternative hypothesis.
Testing of hypotheses
Hypothesis testing involves stating a null hypothesis (H0) and an alternative hypothesis (H1). A test statistic is calculated from sample data and used to determine whether to reject or fail to reject H0. There are two types of errors: Type I rejects a true H0, Type II fails to reject a false H0. The significance level (α) limits Type I error, while power (1- β) measures the test's ability to reject H0 when it is false. Tests can be one-tailed if H1 specifies a direction, or two-tailed. The rejection region defines values where H0 will be rejected.
teast mean one and two sample
This document provides an overview of hypothesis testing, including key concepts like the null and alternative hypotheses, Type I and Type II errors, and the seven steps of hypothesis testing. It explains that the goal is to analyze a sample to determine if a population characteristic is likely or unlikely. The null hypothesis is represented by H0 and states population parameters as equalities, while the alternative hypothesis H1 states inequalities. The document also describes tests for comparing means and proportions between two samples or populations.
Chapter 9 Fundamental of Hypothesis Testing.ppt
- Hypothesis testing involves initially assuming the null hypothesis is true and then examining sample data to determine if it provides strong enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
- There are two main approaches: the rejection region approach which defines critical values based on the level of significance, and the p-value approach which calculates the probability of obtaining the sample results if the null hypothesis is true.
- Type I and Type II errors can occur if the null hypothesis is incorrectly rejected or not rejected, respectively, and there is a tradeoff between the probabilities of each.
testingofhypothesis-150108150611-conversion-gate02.pptx
Hypothesis testing involves making an assumption about an unknown population parameter, called the null hypothesis (H0). A hypothesis test is then conducted by collecting a sample from the population and calculating a test statistic. The test statistic is compared to a critical value to either reject or fail to reject the null hypothesis. There are two types of errors that can occur - a Type I error occurs when a true null hypothesis is rejected, and a Type II error occurs when a false null hypothesis is not rejected. The level of significance and whether the test is one-tailed or two-tailed determine the critical value used for comparison.
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The document discusses hypothesis testing, including the key concepts of the null and alternative hypotheses, types of errors, and approaches to testing hypotheses. It provides examples of hypothesis tests for a population mean. The null hypothesis is initially assumed to be true, and sample data are used to determine if there is sufficient evidence against the null in favor of the alternative hypothesis. The rejection region and p-value approaches are outlined as methods to evaluate the sample data relative to the critical values or significance level and determine whether to reject or fail to reject the null hypothesis.
Study unit 4 (oct 2014)
This document provides an overview of hypothesis testing methodology for one population. It defines key concepts like the null and alternative hypotheses, types of errors, test statistics, significance levels, and rejection regions. The two main approaches to hypothesis testing are presented: the rejection region approach and the p-value approach. Steps for conducting a hypothesis test are outlined, including stating hypotheses, choosing test criteria, collecting data, determining test statistics and p-values, and making conclusions. Examples are provided to illustrate hypothesis tests for means and proportions.
Study unit 4 (oct 2014)
This document provides an overview of hypothesis testing methodology for one population. It defines key concepts like the null and alternative hypotheses, types of errors, test statistics, significance levels, and rejection regions. The two main approaches to hypothesis testing are presented: the rejection region approach and the p-value approach. Steps for conducting a hypothesis test are outlined, including stating hypotheses, choosing test criteria, collecting data, determining test statistics and p-values, and making conclusions. Examples are provided to illustrate hypothesis tests for means and proportions.
Hypothesis_Testing.ppt
1) Hypothesis testing involves making an educated guess about a population parameter and designing a study to analyze sample data to determine if the population characteristic is likely or unlikely.
2) The null hypothesis states what is assumed to be true about the population parameter, while the alternative hypothesis is what would be accepted if the null is rejected. Type I and Type II errors occur when the wrong conclusion is reached.
3) Key aspects of hypothesis testing include defining the test statistic, rejection region, significance level, and whether a one-tailed or two-tailed test is appropriate based on the alternative hypothesis.
Testing of hypotheses
Hypothesis testing involves stating a null hypothesis (H0) and an alternative hypothesis (H1). A test statistic is calculated from sample data and used to determine whether to reject or fail to reject H0. There are two types of errors: Type I rejects a true H0, Type II fails to reject a false H0. The significance level (α) limits Type I error, while power (1- β) measures the test's ability to reject H0 when it is false. Tests can be one-tailed if H1 specifies a direction, or two-tailed. The rejection region defines values where H0 will be rejected.
teast mean one and two sample
This document provides an overview of hypothesis testing, including key concepts like the null and alternative hypotheses, Type I and Type II errors, and the seven steps of hypothesis testing. It explains that the goal is to analyze a sample to determine if a population characteristic is likely or unlikely. The null hypothesis is represented by H0 and states population parameters as equalities, while the alternative hypothesis H1 states inequalities. The document also describes tests for comparing means and proportions between two samples or populations.
Chapter 9 Fundamental of Hypothesis Testing.ppt
- Hypothesis testing involves initially assuming the null hypothesis is true and then examining sample data to determine if it provides strong enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
- There are two main approaches: the rejection region approach which defines critical values based on the level of significance, and the p-value approach which calculates the probability of obtaining the sample results if the null hypothesis is true.
- Type I and Type II errors can occur if the null hypothesis is incorrectly rejected or not rejected, respectively, and there is a tradeoff between the probabilities of each.
testingofhypothesis-150108150611-conversion-gate02.pptx
Hypothesis testing involves making an assumption about an unknown population parameter, called the null hypothesis (H0). A hypothesis test is then conducted by collecting a sample from the population and calculating a test statistic. The test statistic is compared to a critical value to either reject or fail to reject the null hypothesis. There are two types of errors that can occur - a Type I error occurs when a true null hypothesis is rejected, and a Type II error occurs when a false null hypothesis is not rejected. The level of significance and whether the test is one-tailed or two-tailed determine the critical value used for comparison.
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- The document discusses statistical hypothesis testing and introduces key concepts like null hypotheses (H0), alternative hypotheses (H1), Type I and Type II errors, p-values, and rejection regions.
- It provides an example to illustrate a hypothesis test comparing the mean of a sample to a hypothesized population mean, and calculates the test statistic and p-value to determine whether to reject the null hypothesis or not.
- The example tests whether the mean monthly account balance is greater than $170, and finds enough evidence based on the test statistic and p-value to reject the null hypothesis that the mean is less than or equal to $170.
Formulatinghypotheses
The document discusses the concepts and process of formulating and testing hypotheses in business research methodology. It defines key terms related to hypotheses such as the null hypothesis, alternate hypothesis, type I and type II errors, and level of significance. The steps in hypothesis testing are outlined, including formulating the hypotheses, defining a test statistic, determining the distribution of the test statistic, defining the critical region, and making a decision to accept or reject the null hypothesis. Both parametric and non-parametric tests are discussed along with conditions for using z-tests and t-tests.
Formulating Hypotheses
This document provides an overview of key concepts related to formulating and testing hypotheses. It defines a hypothesis as a proposition or claim about a population that can be empirically tested. Hypothesis testing involves examining two opposing hypotheses: the null hypothesis (H0) and alternative hypothesis (Ha). It describes the basic steps of hypothesis testing as formulating the hypotheses, defining a test statistic, determining the distribution of the test statistic, defining the critical region, and making a decision to accept or reject the null hypothesis. Key concepts like type I and type II errors, significance levels, critical values, and one-tailed vs two-tailed tests are also explained. Parametric tests like the z-test, t-test, and
STATISTICS: Hypothesis Testing
This document discusses hypothesis testing, including:
1) The objectives are to formulate statistical hypotheses, discuss types of errors, establish decision rules, and choose appropriate tests.
2) Key symbols and concepts are defined, such as the null and alternative hypotheses, Type I and Type II errors, test statistics like z and t, means, variances, sample sizes, and significance levels.
3) The two types of errors in hypothesis testing are discussed. Hypothesis tests can result in correct decisions or two types of errors when the null hypothesis is true or false.
4) Steps in hypothesis testing are outlined, including formulating hypotheses, specifying a significance level, choosing a test statistic, establishing a
Business Statistics Chapter 9
Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
Chapter Topic:
Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
Potential Hypothesis-Testing Pitfalls and Ethical Issues
Introduction to hypothesis testing ppt @ bec doms
This document introduces hypothesis testing, including:
- Formulating null and alternative hypotheses for tests involving population means and proportions
- Using test statistics, critical values, and p-values to test hypotheses
- Defining Type I and Type II errors and their probabilities
- Examples of hypothesis tests for means (using z-tests and t-tests) and proportions (using z-tests) are provided to illustrate the concepts.
Hypothesis testing
This document discusses hypothesis testing. It defines key terms like the null hypothesis (Ho), alternative hypothesis (H1), type 1 and type 2 errors, significance level, test statistics, critical values, rejection regions, and one-tailed vs two-tailed tests. It provides examples of how to formulate hypotheses, determine appropriate test statistics, establish critical regions, and make conclusions based on computed test values for both known and unknown population variances with one and two sample tests concerning means.
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The document discusses hypothesis testing, including:
- The null hypothesis is initially assumed to be true, and data is examined to determine if there is strong enough evidence in favor of the alternative hypothesis to reject the null.
- There are two types of errors - type I errors where a true null hypothesis is incorrectly rejected, and type II errors where a false null hypothesis is not rejected. The significance level determines the likelihood of type I errors.
- Hypothesis tests can be conducted using either the rejection region approach which defines critical values, or the p-value approach which directly calculates the probability of obtaining the sample results if the null is true.
Hypothesis
This document provides an overview of hypothesis testing. It defines key terms like the null hypothesis (H0), alternative hypothesis (H1), type I and type II errors, significance level, p-values, and test statistics. It explains the basic steps in hypothesis testing as testing a claim about a population parameter by collecting a sample, determining the appropriate test statistic based on the sampling distribution, and comparing it to critical values to reject or fail to reject the null hypothesis. Examples are provided to demonstrate hypothesis tests for a mean when the population standard deviation is known or unknown.
Formulating hypotheses
The document discusses key concepts related to formulating and testing hypotheses, including:
- Null and alternative hypotheses, which are mutually exclusive statements tested through sample analysis.
- Type I and Type II errors that can occur when making decisions to accept or reject the null hypothesis.
- The level of significance, critical region, and test statistics used to determine whether to reject the null hypothesis.
- The differences between one-tailed and two-tailed tests, parametric vs. non-parametric tests, and one-sample vs. two-sample tests.
HYPOTHESIS TESTING.ppt
This document provides an introduction to hypothesis testing. It discusses key concepts such as the null and alternative hypotheses, types of errors, levels of significance, test statistics, p-values, and decision rules. Examples are provided to demonstrate how to state hypotheses, identify the type of test, find critical values and rejection regions, calculate test statistics and p-values, and make decisions to reject or fail to reject the null hypothesis based on these concepts. The steps outlined include stating the hypotheses, specifying the significance level, determining the test statistic and sampling distribution, finding the p-value or using rejection regions to make a decision, and interpreting what the decision means for the original claim.
hypothesis test
This document provides an overview of estimation and hypothesis testing. It defines key statistical concepts like population and sample, parameters and estimates, and introduces the two main methods in inferential statistics - estimation and hypothesis testing.
It explains that hypothesis testing involves setting a null hypothesis (H0) and an alternative hypothesis (Ha), calculating a test statistic, determining a p-value, and making a decision to accept or reject the null hypothesis based on the p-value and significance level. The four main steps of hypothesis testing are outlined as setting hypotheses, calculating a test statistic, determining the p-value, and making a conclusion.
Examples are provided to demonstrate left-tailed, right-tailed, and two-tailed hypothesis tests
Hypothesis Testing (Statistical Significance)1Hypo.docx
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each group
Decision Rule:
a. If the confidence interval (CI) overlap, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) do not include the null, then the decision must be to reject the H0.
7
2.Test Statistic
Calculate the test statistic (TS)
Obtain the critical value (CV) from the reference table
Decision Rule:
a. If the test statistic is in the FTR region, then the decision must be to fail to reject the H0.
b. If the test statistic is in the rejection region, then the decision must be to reject the H0.
FTR
CV
TS
Since the test statistic is in the rejection region, reject the H0
FTR
CV
Since the test statistic is in the fail to reject region, fail to reject the H0
TS
CV
CV
8
3. P-Value
Choose α
Calculate value of test statistic from your data
Calculate P- value from test statistic
Decision Rule:
a. If the p-value is less than the level of significance, α, then the decision m.
hypothesis_testing-ch9-39-14402.pdf
1. The document discusses the basic principles of hypothesis testing, including stating the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining critical values, and making a decision to reject or fail to reject the null hypothesis.
2. It outlines the five steps of hypothesis testing: state hypotheses, select significance level, select test statistic, determine critical value, and make a decision.
3. Key terms discussed include type I and type II errors, significance levels, critical values, test statistics such as z and t, and the decision to reject or fail to reject the null hypothesis.
hypothesis-tesing.pdf
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 null hypothesis. If the sample statistic is sufficiently different from the null hypothesis, 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 statistic is greater than or less than the null hypothesis, or two-tailed, testing if it is significantly different in either direction.
Int 150 The Moral Instinct”1. Most cultures agree that abus.docx
Int 150
“The Moral Instinct”
1. Most cultures agree that abusing innocent people is wrong. True or false
2. Young children have a sense of morality. True or false (example)?
3. Emotional reasoning trumps rationalizing. True or false (explain)
4. According to the article, psychopathy or moral misbehavior (like rape) is more environmental than genetic. True or false (example)
5. Explain the point about the British schoolteacher in Sudan.
6. Name three things anthropologists believe all people share, in addition to thinking it’s bad to harm others and good to help them.
a.
b.
c.
7. What is reciprocal altruism?
8. How does the psychologist Tetlock explain the outrage of American college students at the thought that adoption agencies should place children with couples willing to pay the most?
9. Discuss: A love for children and sense of justice is just an expression of our innate sense of preserving our genes for future generations (Darwin)
10. What does the author warn about the arguments regarding climate change?
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each gro.
HYPOTHESIS TESTING 20200702.pptx
This document discusses hypothesis testing. It defines hypothesis as an assumption or statement that may or may not be true. The key points covered include:
- Types of hypotheses include null and alternative hypotheses
- Errors in hypothesis testing include Type I errors of rejecting a true null hypothesis and Type II errors of failing to reject a false null hypothesis
- The hypothesis testing process involves setting hypotheses, significance level, determining test statistics, critical regions, computing test statistics, and making a decision to accept or reject the null hypothesis
Testing of Hypothesis, p-value, Gaussian distribution, null hypothesis
This document provides an overview of key concepts in statistical hypothesis testing. It defines what a hypothesis is, the different types of hypotheses (null, alternative, one-tailed, two-tailed), and statistical terms used in hypothesis testing like test statistics, critical regions, significance levels, critical values, type I and type II errors. It also explains the decision making process in hypothesis testing, such as rejecting or failing to reject the null hypothesis based on whether the test statistic falls within the critical region or if the p-value is less than the significance level.
Hypothesis testing1
This document provides an overview of hypothesis testing. It begins by defining hypothesis testing and listing the typical steps: 1) formulating the null and alternative hypotheses, 2) computing the test statistic, 3) determining the p-value and interpretation, and 4) specifying the significance level. It then discusses different types of hypothesis tests for claims about a mean when the population standard deviation is known or unknown, as well as tests for claims about a population proportion. Examples are provided for each type of test to demonstrate how to apply the steps. The document aims to explain the concept and process of hypothesis testing for making data-driven decisions about statistical claims.
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Stream of Consciousness in the novel ‘ To The Lighthouse’
Paper The Modernist Literature
Topic Stream of Consciousness in
the novel ‘To The Lighthouse’
Name Avani N. Dave
Roll No. 2
Class M.A. Sem. 3
Submitted to Dr. Dilip Barad
Department of English
MK.Bhavnagar University
Introduction
Virginia woolf, one of the prominent representative Of Modernist novelist in England, has contributed significantly to the development of modern novel in both theory and practice. She abandoned traditional fictional devices and formulated her own distinctive techniques. The novels of woolf tend to be less concerned with outward reality than with the inner life. Her masterpiece, to the Lighthouse, serves as an excellent sample in analyzing woolf’s literary theory and her experimental techniques.
Origin of the Word
The phrase “Stream of Consciousness” was coined by William James 1 to describe the flow of thoughts of the waking mind. Subsequently his phrase began to be used in a literary context to describe the narrative method by which certain novelists have described the unspoken thoughts and feelings of their characters, without resorting to objectives description or conventional dialogue. James Joyce was a pioneer in using this technique in his novels of which the best known are Ulysses and The Portrait of the Artist as a Young Man. And this technique was also used by Virginia Woolf. The related phrase “interior monologue” is used to describe the inner movement of Consciousness in a character’s mind. A famous example of the interior monologue is the opening pages of Mrs. Dalloway. The use of devices of the stream of Consciousness and the interior monologue marks a revolution in the form of the novel because through these devices the author can represent the flux of a character’s thoughts, impressions, and emotions and reminiscences, often without any logical Sequence.
Virginia Woolf and To The Lighthouse
When we mention Virginia Woolf’s ‘To The Lighthouse’, it’s very natural to talk about her stream of consciousness technique. In this novel, the structure of external objective events is demised in scope and scale, or almost e completely dissolved. It is composed of the continual activity of characters’ consciousness and shower of impressions. External events occupy little space in the novel the writer as an omniscient narrator has almost completely vanished and almost everything stated appears by the way of reflection in the consciousness of the dramatic characters and the novel does not progress on “what – happens – next” basis, but rather moves forward through a series of scenes arranged according to a sequence of selected moments of consciousness and the techniques to
Introduction of Entrepreneurship and financial management.pptx
q Entrepreneurship is a buzz word these days. Everyone is talking about entrepreneurship or wants to be an entrepreneur. q Entrepreneurship is all about doing your own business and entrepreneur is a person who sets up a business
q Seek or create a job!
• Why all entities like government, educational and financial institution are supporting entrepreneurship?
• What if all graduates students are job seekers?
• What if no one is creating a firm?
• Then, who will create jobs?
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This document discusses hypothesis testing, including:
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Hypothesis Testing Methodology
Z Test for the Mean ( Known)
p-Value Approach to Hypothesis Testing
Connection to Confidence Interval Estimation
One-Tail Tests
t Test for the Mean ( Unknown)
Z Test for the Proportion
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This document introduces hypothesis testing, including:
- Formulating null and alternative hypotheses for tests involving population means and proportions
- Using test statistics, critical values, and p-values to test hypotheses
- Defining Type I and Type II errors and their probabilities
- Examples of hypothesis tests for means (using z-tests and t-tests) and proportions (using z-tests) are provided to illustrate the concepts.
Hypothesis testing
This document discusses hypothesis testing. It defines key terms like the null hypothesis (Ho), alternative hypothesis (H1), type 1 and type 2 errors, significance level, test statistics, critical values, rejection regions, and one-tailed vs two-tailed tests. It provides examples of how to formulate hypotheses, determine appropriate test statistics, establish critical regions, and make conclusions based on computed test values for both known and unknown population variances with one and two sample tests concerning means.
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The document discusses hypothesis testing, including:
- The null hypothesis is initially assumed to be true, and data is examined to determine if there is strong enough evidence in favor of the alternative hypothesis to reject the null.
- There are two types of errors - type I errors where a true null hypothesis is incorrectly rejected, and type II errors where a false null hypothesis is not rejected. The significance level determines the likelihood of type I errors.
- Hypothesis tests can be conducted using either the rejection region approach which defines critical values, or the p-value approach which directly calculates the probability of obtaining the sample results if the null is true.
Hypothesis
This document provides an overview of hypothesis testing. It defines key terms like the null hypothesis (H0), alternative hypothesis (H1), type I and type II errors, significance level, p-values, and test statistics. It explains the basic steps in hypothesis testing as testing a claim about a population parameter by collecting a sample, determining the appropriate test statistic based on the sampling distribution, and comparing it to critical values to reject or fail to reject the null hypothesis. Examples are provided to demonstrate hypothesis tests for a mean when the population standard deviation is known or unknown.
Formulating hypotheses
The document discusses key concepts related to formulating and testing hypotheses, including:
- Null and alternative hypotheses, which are mutually exclusive statements tested through sample analysis.
- Type I and Type II errors that can occur when making decisions to accept or reject the null hypothesis.
- The level of significance, critical region, and test statistics used to determine whether to reject the null hypothesis.
- The differences between one-tailed and two-tailed tests, parametric vs. non-parametric tests, and one-sample vs. two-sample tests.
HYPOTHESIS TESTING.ppt
This document provides an introduction to hypothesis testing. It discusses key concepts such as the null and alternative hypotheses, types of errors, levels of significance, test statistics, p-values, and decision rules. Examples are provided to demonstrate how to state hypotheses, identify the type of test, find critical values and rejection regions, calculate test statistics and p-values, and make decisions to reject or fail to reject the null hypothesis based on these concepts. The steps outlined include stating the hypotheses, specifying the significance level, determining the test statistic and sampling distribution, finding the p-value or using rejection regions to make a decision, and interpreting what the decision means for the original claim.
hypothesis test
This document provides an overview of estimation and hypothesis testing. It defines key statistical concepts like population and sample, parameters and estimates, and introduces the two main methods in inferential statistics - estimation and hypothesis testing.
It explains that hypothesis testing involves setting a null hypothesis (H0) and an alternative hypothesis (Ha), calculating a test statistic, determining a p-value, and making a decision to accept or reject the null hypothesis based on the p-value and significance level. The four main steps of hypothesis testing are outlined as setting hypotheses, calculating a test statistic, determining the p-value, and making a conclusion.
Examples are provided to demonstrate left-tailed, right-tailed, and two-tailed hypothesis tests
Hypothesis Testing (Statistical Significance)1Hypo.docx
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each group
Decision Rule:
a. If the confidence interval (CI) overlap, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) do not include the null, then the decision must be to reject the H0.
7
2.Test Statistic
Calculate the test statistic (TS)
Obtain the critical value (CV) from the reference table
Decision Rule:
a. If the test statistic is in the FTR region, then the decision must be to fail to reject the H0.
b. If the test statistic is in the rejection region, then the decision must be to reject the H0.
FTR
CV
TS
Since the test statistic is in the rejection region, reject the H0
FTR
CV
Since the test statistic is in the fail to reject region, fail to reject the H0
TS
CV
CV
8
3. P-Value
Choose α
Calculate value of test statistic from your data
Calculate P- value from test statistic
Decision Rule:
a. If the p-value is less than the level of significance, α, then the decision m.
hypothesis_testing-ch9-39-14402.pdf
1. The document discusses the basic principles of hypothesis testing, including stating the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining critical values, and making a decision to reject or fail to reject the null hypothesis.
2. It outlines the five steps of hypothesis testing: state hypotheses, select significance level, select test statistic, determine critical value, and make a decision.
3. Key terms discussed include type I and type II errors, significance levels, critical values, test statistics such as z and t, and the decision to reject or fail to reject the null hypothesis.
hypothesis-tesing.pdf
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 null hypothesis. If the sample statistic is sufficiently different from the null hypothesis, 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 statistic is greater than or less than the null hypothesis, or two-tailed, testing if it is significantly different in either direction.
Int 150 The Moral Instinct”1. Most cultures agree that abus.docx
Int 150
“The Moral Instinct”
1. Most cultures agree that abusing innocent people is wrong. True or false
2. Young children have a sense of morality. True or false (example)?
3. Emotional reasoning trumps rationalizing. True or false (explain)
4. According to the article, psychopathy or moral misbehavior (like rape) is more environmental than genetic. True or false (example)
5. Explain the point about the British schoolteacher in Sudan.
6. Name three things anthropologists believe all people share, in addition to thinking it’s bad to harm others and good to help them.
a.
b.
c.
7. What is reciprocal altruism?
8. How does the psychologist Tetlock explain the outrage of American college students at the thought that adoption agencies should place children with couples willing to pay the most?
9. Discuss: A love for children and sense of justice is just an expression of our innate sense of preserving our genes for future generations (Darwin)
10. What does the author warn about the arguments regarding climate change?
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each gro.
HYPOTHESIS TESTING 20200702.pptx
This document discusses hypothesis testing. It defines hypothesis as an assumption or statement that may or may not be true. The key points covered include:
- Types of hypotheses include null and alternative hypotheses
- Errors in hypothesis testing include Type I errors of rejecting a true null hypothesis and Type II errors of failing to reject a false null hypothesis
- The hypothesis testing process involves setting hypotheses, significance level, determining test statistics, critical regions, computing test statistics, and making a decision to accept or reject the null hypothesis
Testing of Hypothesis, p-value, Gaussian distribution, null hypothesis
This document provides an overview of key concepts in statistical hypothesis testing. It defines what a hypothesis is, the different types of hypotheses (null, alternative, one-tailed, two-tailed), and statistical terms used in hypothesis testing like test statistics, critical regions, significance levels, critical values, type I and type II errors. It also explains the decision making process in hypothesis testing, such as rejecting or failing to reject the null hypothesis based on whether the test statistic falls within the critical region or if the p-value is less than the significance level.
Hypothesis testing1
This document provides an overview of hypothesis testing. It begins by defining hypothesis testing and listing the typical steps: 1) formulating the null and alternative hypotheses, 2) computing the test statistic, 3) determining the p-value and interpretation, and 4) specifying the significance level. It then discusses different types of hypothesis tests for claims about a mean when the population standard deviation is known or unknown, as well as tests for claims about a population proportion. Examples are provided for each type of test to demonstrate how to apply the steps. The document aims to explain the concept and process of hypothesis testing for making data-driven decisions about statistical claims.
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Data Science : Unit-I -Hypothesis and Inferences.pptx
Data Science : Unit-I -Hypothesis and Inferences.pptx
Hypothesis Testing (Statistical Significance)1Hypo.docx
Hypothesis Testing (Statistical Significance)1Hypo.docx
Int 150 The Moral Instinct”1. Most cultures agree that abus.docx
Int 150 The Moral Instinct”1. Most cultures agree that abus.docx
Testing of Hypothesis, p-value, Gaussian distribution, null hypothesis
Testing of Hypothesis, p-value, Gaussian distribution, null hypothesis
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Stream of Consciousness in the novel ‘ To The Lighthouse’
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Topic Stream of Consciousness in
the novel ‘To The Lighthouse’
Name Avani N. Dave
Roll No. 2
Class M.A. Sem. 3
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Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
Candidate young stellar objects in the S-cluster: Kinematic analysis of a sub...
Context. The observation of several L-band emission sources in the S cluster has led to a rich discussion of their nature. However, a definitive answer to the classification of the dusty objects requires an explanation for the detection of compact Doppler-shifted Brγ emission. The ionized hydrogen in combination with the observation of mid-infrared L-band continuum emission suggests that most of these sources are embedded in a dusty envelope. These embedded sources are part of the S-cluster, and their relationship to the S-stars is still under debate. To date, the question of the origin of these two populations has been vague, although all explanations favor migration processes for the individual cluster members. Aims. This work revisits the S-cluster and its dusty members orbiting the supermassive black hole SgrA* on bound Keplerian orbits from a kinematic perspective. The aim is to explore the Keplerian parameters for patterns that might imply a nonrandom distribution of the sample. Additionally, various analytical aspects are considered to address the nature of the dusty sources. Methods. Based on the photometric analysis, we estimated the individual H−K and K−L colors for the source sample and compared the results to known cluster members. The classification revealed a noticeable contrast between the S-stars and the dusty sources. To fit the flux-density distribution, we utilized the radiative transfer code HYPERION and implemented a young stellar object Class I model. We obtained the position angle from the Keplerian fit results; additionally, we analyzed the distribution of the inclinations and the longitudes of the ascending node. Results. The colors of the dusty sources suggest a stellar nature consistent with the spectral energy distribution in the near and midinfrared domains. Furthermore, the evaporation timescales of dusty and gaseous clumps in the vicinity of SgrA* are much shorter ( 2yr) than the epochs covered by the observations (≈15yr). In addition to the strong evidence for the stellar classification of the D-sources, we also find a clear disk-like pattern following the arrangements of S-stars proposed in the literature. Furthermore, we find a global intrinsic inclination for all dusty sources of 60 ± 20◦, implying a common formation process. Conclusions. The pattern of the dusty sources manifested in the distribution of the position angles, inclinations, and longitudes of the ascending node strongly suggests two different scenarios: the main-sequence stars and the dusty stellar S-cluster sources share a common formation history or migrated with a similar formation channel in the vicinity of SgrA*. Alternatively, the gravitational influence of SgrA* in combination with a massive perturber, such as a putative intermediate mass black hole in the IRS 13 cluster, forces the dusty objects and S-stars to follow a particular orbital arrangement. Key words. stars: black holes– stars: formation– Galaxy: center– galaxies: star formation
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdf
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx
Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.
SDSS1335+0728: The awakening of a ∼ 106M⊙ black hole⋆
Context. The early-type galaxy SDSS J133519.91+072807.4 (hereafter SDSS1335+0728), which had exhibited no prior optical variations during the preceding two decades, began showing significant nuclear variability in the Zwicky Transient Facility (ZTF) alert stream from December 2019 (as ZTF19acnskyy). This variability behaviour, coupled with the host-galaxy properties, suggests that SDSS1335+0728 hosts a ∼ 106M⊙ black hole (BH) that is currently in the process of ‘turning on’. Aims. We present a multi-wavelength photometric analysis and spectroscopic follow-up performed with the aim of better understanding the origin of the nuclear variations detected in SDSS1335+0728. Methods. We used archival photometry (from WISE, 2MASS, SDSS, GALEX, eROSITA) and spectroscopic data (from SDSS and LAMOST) to study the state of SDSS1335+0728 prior to December 2019, and new observations from Swift, SOAR/Goodman, VLT/X-shooter, and Keck/LRIS taken after its turn-on to characterise its current state. We analysed the variability of SDSS1335+0728 in the X-ray/UV/optical/mid-infrared range, modelled its spectral energy distribution prior to and after December 2019, and studied the evolution of its UV/optical spectra. Results. From our multi-wavelength photometric analysis, we find that: (a) since 2021, the UV flux (from Swift/UVOT observations) is four times brighter than the flux reported by GALEX in 2004; (b) since June 2022, the mid-infrared flux has risen more than two times, and the W1−W2 WISE colour has become redder; and (c) since February 2024, the source has begun showing X-ray emission. From our spectroscopic follow-up, we see that (i) the narrow emission line ratios are now consistent with a more energetic ionising continuum; (ii) broad emission lines are not detected; and (iii) the [OIII] line increased its flux ∼ 3.6 years after the first ZTF alert, which implies a relatively compact narrow-line-emitting region. Conclusions. We conclude that the variations observed in SDSS1335+0728 could be either explained by a ∼ 106M⊙ AGN that is just turning on or by an exotic tidal disruption event (TDE). If the former is true, SDSS1335+0728 is one of the strongest cases of an AGNobserved in the process of activating. If the latter were found to be the case, it would correspond to the longest and faintest TDE ever observed (or another class of still unknown nuclear transient). Future observations of SDSS1335+0728 are crucial to further understand its behaviour. Key words. galaxies: active– accretion, accretion discs– galaxies: individual: SDSS J133519.91+072807.4
Methods of grain storage Structures in India.pdf
•Post-harvestlossesaccountforabout10%oftotalfoodgrainsduetounscientificstorage,insects,rodents,micro-organismsetc.,
•Totalfoodgrainproductioninindiais311milliontonnesandstorageis145mt.InIndia,annualstoragelosseshavebeenestimated14mtworthofRs.7,000croreinwhichinsectsaloneaccountfornearlyRs.1,300crores.
•InIndiaoutofthetotalproduction,about30%ismarketablesurplus
•Remaining70%isretainedandstoredbyfarmersforconsumption,seed,feed.Hence,growerneedstoragefacilitytoholdaportionofproducetosellwhenthemarketingpriceisfavourable
•TradersandCo-operativesatmarketcentresneedstoragestructurestoholdgrainswhenthetransportfacilityisinadequate
TOPIC OF DISCUSSION: CENTRIFUGATION SLIDESHARE.pptx
Centrifugation is a powerful technique used in laboratories to separate components of a heterogeneous mixture based on their density. This process utilizes centrifugal force to rapidly spin samples, causing denser particles to migrate outward more quickly than lighter ones. As a result, distinct layers form within the sample tube, allowing for easy isolation and purification of target substances.
Male reproduction physiology by Suyash Garg .pptx
Physiology of Male reproduction.
Video mentioned at page no. 23 as summary for better understanding
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- 1. © 1999 Prentice-Hall, Inc. Chap. 8 - 1 •General procedure for hypothesis testing Presentd by Iram hassan
- 2. © 1999 Prentice-Hall, Inc. Chap. 8 - 2 A hypothesis is an assumption about the population parameter. A parameter is a Population mean or proportion The parameter must be identified before analysis. I assume the mean GPA of this class is 3.5! © 1984-1994 T/Maker Co. What is a Hypothesis?
- 3. © 1999 Prentice-Hall, Inc. Chap. 8 - 3 • States the Assumption (numerical) to be tested e.g. The average # TV sets in US homes is at least 3 (H0: 3) • Begin with the assumption that the null hypothesis is TRUE. (Similar to the notion of innocent until proven guilty) The Null Hypothesis, H0 •Always contains the ‘ = ‘ sign •The Null Hypothesis may or may not be rejected.
- 4. © 1999 Prentice-Hall, Inc. Chap. 8 - 4 • Is the opposite of the null hypothesis e.g. The average # TV sets in US homes is less than 3 (H1: < 3) • Never contains the ‘=‘ sign • The Alternative Hypothesis may or may not be accepted The Alternative Hypothesis, H1
- 5. © 1999 Prentice-Hall, Inc. Chap. 8 - 5 Steps: State the Null Hypothesis (H0: 3) State its opposite, the Alternative Hypothesis (H1: < 3) Hypotheses are mutually exclusive & exhaustive Sometimes it is easier to form the alternative hypothesis first. Identify the Problem
- 6. © 1999 Prentice-Hall, Inc. Chap. 8 - 6 Population Assume the population mean age is 50. (Null Hypothesis) REJECT The Sample Mean Is 20 Sample Null Hypothesis 50? 20 X Is Hypothesis Testing Process No, not likely!
- 7. © 1999 Prentice-Hall, Inc. Chap. 8 - 7 • The significance level of a test is the probabilty used as a standard rejecting a null hypothesis Ho when Null Hypothesis Is True Called Rejection Region of Sampling Distribution • Designated a (alpha) Typical values are 0.01, 0.05, 0.10 • Selected by the Researcher at the Start • Provides the Critical Value(s) of the Test 2.Level of Significance, a
- 8. © 1999 Prentice-Hall, Inc. Chap. 8 - 8 Level of Significance, aand the Rejection Region H0: 3 H1: < 3 0 0 0 H0: 3 H1: > 3 H0: 3 H1: 3 a a a/2 Critical Value(s) Rejection Regions
- 9. © 1999 Prentice-Hall, Inc. Chap. 8 - 9 • Type I Error Reject True Null Hypothesis Has Serious Consequences Probability of Type I Error Is a Called Level of Significance • Type II Error Do Not Reject False Null Hypothesis Probability of Type II Error Is b (Beta) Errors in Making Decisions
- 10. © 1999 Prentice-Hall, Inc. Chap. 8 - 10 H0: Innocent Jury Trial Hypothesis Test Actual Situation Actual Situation Verdict Innocent Guilty Decision H0 True H0 False Innocent Correct Error Do Not Reject H0 1 - a Type II Error (b ) Guilty Error Correct Reject H0 Type I Error (a ) Power (1 - b) Result Possibilities
- 11. © 1999 Prentice-Hall, Inc. Chap. 8 - 11 • A test of statistics is a rule or procedure by which sample results are used to decide whethere to accept or reject the null hypothesis. • e.g: z test,t test,f test,ANOVA etc 3.Test Statistics
- 12. © 1999 Prentice-Hall, Inc. Chap. 8 - 12 • Probability of Obtaining a Test Statistic More Extreme or ) than Actual Sample Value Given H0 Is True • Called Observed Level of Significance Smallest Value of a H0 Can Be Rejected • Used to Make Rejection Decision If p value a Do Not Reject H0 If p value < a, Reject H0 p Value Test
- 13. © 1999 Prentice-Hall, Inc. Chap. 8 - 13 4.Critical region • determine the rejection or crtical region n such a way that the probabilty of rejecting the null hypothesis Ho,if it is true,is equal to the significance level,α.the location of the crtical region depends upon the form of H1.the significance level will seperate the acceptance region from the rejection region. • one tail and two tail test
- 14. © 1999 Prentice-Hall, Inc. Chap. 8 - 14 1. State H0 H0 : 3 2. State H1 H1 : <3 3. Choose a a = .05 4. Choose n n = 100 5. Choose Test: Z Test (or p Value) Hypothesis Testing: Steps Test the Assumption that the true mean # of TV sets in US homes is at least 3.
- 15. © 1999 Prentice-Hall, Inc. Chap. 8 - 15 5.computation/calculation compute the value of test statistics from the sample data in order to decide whethere to accept or reject the null hypothesis.
- 16. © 1999 Prentice-Hall, Inc. Chap. 8 - 16 6.Decision a.reject the null hypothesis Ho,if computed value of the test statistics falls in the rejection region and conclude that Ho is true b.accept the null hypothesis Ho,otherwise.
- 17. © 1999 Prentice-Hall, Inc. Chap. 8 - 17 Z 0 a Reject H0 Z 0 Reject H0 a H0: H1: < 0 H0: 0 H1: > 0 Must Be Significantly Below = 0 Small values don’t contradict H0 Don’t Reject H0! Rejection Region
- 18. © 1999 Prentice-Hall, Inc. Chap. 8 - 18 a= 0.025 n = 25 Critical Value: 1.645 Test Statistic: Decision: Conclusion: Do Not Reject at a = .05 No Evidence True Mean Is More than 368 Z 0 1.645 .05 Reject Example Solution: One Tail H0: 368 H1: > 368 50 . 1 n X Z
- 19. © 1999 Prentice-Hall, Inc. Chap. 8 - 19 0 1.50 Z Reject (p Value = 0.0668) (a = 0.05). Do Not Reject. p Value = 0.0668 a= 0.05 Test Statistic Is In the Do Not Reject Region p Value Solution