Hypothesis testing
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The document outlines the steps for hypothesis testing which include: 1) Formulating the null and alternative hypotheses 2) Selecting an appropriate statistical test such as chi-square or ANOVA 3) Choosing the level of significance 4) Collecting and analyzing data to calculate a test statistic 5) Comparing the test statistic to the critical value to determine whether to reject or fail to reject the null hypothesis 6) Drawing a conclusion about the research question being tested
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This document contains an assignment for a statistics course covering various topics in statistics. It includes 6 questions assessing different statistical concepts. Question 1 asks students to describe the functions and applications of statistics. Question 2 covers probability, asking students to explain approaches to defining probability and give examples of addition and multiplication rules. Question 3 involves hypothesis testing procedures and components of time series. Question 4 is about chi-square tests - their meaning, applications, and conditions of use. Question 5 examines business forecasting objectives and theories. Finally, question 6 addresses analysis of variance assumptions and asks students to perform a hypothesis test on sample data.
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03 Design of Experiments - Factor prioritization
Before starting a statistical experimental design, it is helpful to collect and compile all possible influencing variables. This procedure not only helps to identify the important factors, but also ensures that knowledge will be secured in the team. Furthermore, the influence of possibly underestimated factors is clarified and evaluated. Ideally, only after such an assessment are priorities methodically derived. Depending on the challenge, it is appropriate to use different methods and approaches. In this collection of slides, I have compiled my favourite methods and tools from the DFSS context.
Numerical Analysis And Linear Algebra
1. Numerical analysis provides approximate solutions to complex mathematical problems through repeated calculations. It is used when analytical solutions are not possible or too complex.
2. The document discusses the importance of numerical analysis in engineering and science for solving real-world problems. It also defines key concepts like errors, significant digits, and accuracy in numerical analysis.
3. Numerical methods allow finding approximate solutions to problems described by mathematical models through simple arithmetic operations. They are important when analytical solutions are not available.
Chapter 10
This document outlines the steps for hypothesis testing, including:
1. Defining the null and alternative hypotheses (H0 and H1). H0 is presumed true while H1 has the burden of proof.
2. Conducting a 5-step hypothesis testing procedure: state hypotheses, select significance level, select test statistic, formulate decision rule, make decision and interpret.
3. Distinguishing between one-tailed and two-tailed tests. Keywords in the problem statement determine if it is left-tailed, right-tailed, or two-tailed.
4. Examples are provided for testing hypotheses about population means when the population standard deviation is known or unknown, and for testing hypotheses about
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.
Chapter 10
This chapter discusses hypothesis testing and its key concepts. It defines a hypothesis as a statement about a population parameter that is tested. The five steps of hypothesis testing are outlined as defining the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining a decision rule, and making a conclusion. The differences between one-tailed and two-tailed tests are explained. Examples are provided for conducting hypothesis tests on population means and proportions. The chapter also defines Type I and Type II errors and how to compute the probability of a Type II error.
1192012 155942 f023_=_statistical_inference
Statistics is used to summarize, analyze, and interpret groups of numeric data through descriptive and inferential techniques. Descriptive statistics describe data, while inferential statistics allow inferences to be made about a population based on a sample. Hypothesis testing involves setting up null and alternative hypotheses, choosing a test statistic, determining critical values, and deciding whether to reject the null hypothesis. Z-tests are used for large samples, while t-tests are used for small samples. These tests can be applied to compare means, proportions, or paired samples.
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Mb0040
This document contains an assignment for a statistics course covering various topics in statistics. It includes 6 questions assessing different statistical concepts. Question 1 asks students to describe the functions and applications of statistics. Question 2 covers probability, asking students to explain approaches to defining probability and give examples of addition and multiplication rules. Question 3 involves hypothesis testing procedures and components of time series. Question 4 is about chi-square tests - their meaning, applications, and conditions of use. Question 5 examines business forecasting objectives and theories. Finally, question 6 addresses analysis of variance assumptions and asks students to perform a hypothesis test on sample data.
S01 Shainin component swap, DoE
The document describes the technique of component swap analysis to identify the root causes of issues in complex systems. It involves systematically disassembling representative good and bad devices into their components, recombining the components in different configurations, and testing the recombined devices to evaluate the influence of each component and interactions on device performance. The goal is to prioritize the components and factors that most significantly impact the problem for further investigation using techniques like variable analysis or design of experiments.
03 Design of Experiments - Factor prioritization
Before starting a statistical experimental design, it is helpful to collect and compile all possible influencing variables. This procedure not only helps to identify the important factors, but also ensures that knowledge will be secured in the team. Furthermore, the influence of possibly underestimated factors is clarified and evaluated. Ideally, only after such an assessment are priorities methodically derived. Depending on the challenge, it is appropriate to use different methods and approaches. In this collection of slides, I have compiled my favourite methods and tools from the DFSS context.
Numerical Analysis And Linear Algebra
1. Numerical analysis provides approximate solutions to complex mathematical problems through repeated calculations. It is used when analytical solutions are not possible or too complex.
2. The document discusses the importance of numerical analysis in engineering and science for solving real-world problems. It also defines key concepts like errors, significant digits, and accuracy in numerical analysis.
3. Numerical methods allow finding approximate solutions to problems described by mathematical models through simple arithmetic operations. They are important when analytical solutions are not available.
Chapter 10
This document outlines the steps for hypothesis testing, including:
1. Defining the null and alternative hypotheses (H0 and H1). H0 is presumed true while H1 has the burden of proof.
2. Conducting a 5-step hypothesis testing procedure: state hypotheses, select significance level, select test statistic, formulate decision rule, make decision and interpret.
3. Distinguishing between one-tailed and two-tailed tests. Keywords in the problem statement determine if it is left-tailed, right-tailed, or two-tailed.
4. Examples are provided for testing hypotheses about population means when the population standard deviation is known or unknown, and for testing hypotheses about
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.
Chapter 10
This chapter discusses hypothesis testing and its key concepts. It defines a hypothesis as a statement about a population parameter that is tested. The five steps of hypothesis testing are outlined as defining the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining a decision rule, and making a conclusion. The differences between one-tailed and two-tailed tests are explained. Examples are provided for conducting hypothesis tests on population means and proportions. The chapter also defines Type I and Type II errors and how to compute the probability of a Type II error.
1192012 155942 f023_=_statistical_inference
Statistics is used to summarize, analyze, and interpret groups of numeric data through descriptive and inferential techniques. Descriptive statistics describe data, while inferential statistics allow inferences to be made about a population based on a sample. Hypothesis testing involves setting up null and alternative hypotheses, choosing a test statistic, determining critical values, and deciding whether to reject the null hypothesis. Z-tests are used for large samples, while t-tests are used for small samples. These tests can be applied to compare means, proportions, or paired samples.
Chapter 10 One sample test of hypothesis.ppt
The passage discusses the importance of copyright and how it protects original works of authorship such as books, music, art, and movies. Copyright gives the creator exclusive rights to make copies, distribute copies, make derivative works, perform publicly, and display publicly. These rights help ensure that creators can benefit financially from their works and have the incentive to create new works.
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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
This document outlines the steps for conducting a hypothesis test using the classical or critical value method for a one-sample case. It discusses the objectives, elements, and steps of hypothesis testing. The key elements are the null and alternative hypotheses, significance level, critical values of the test statistic, and the critical region used to determine whether to reject or fail to reject the null hypothesis. An example walks through applying the steps, which include formulating hypotheses, selecting a test statistic, establishing the critical region, computing the test statistic, and making a decision. The document emphasizes understanding hypothesis testing procedures and being able to apply the critical value method to real-life problems.
Course Project, Part IIntroduction(REMOVE THIS LINE PRIOR
Course Project, Part I
Introduction
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Summarize what you have learned about confidence intervals. Discuss why it would be important to know the population mean of the data used for this term. Is this an important health measure?)
Sample Data
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: List ALL of the sample data in the table below.)
Directions:
1. Use the table above to create an 80%, 95%, and 99% confidence interval.
2. Choose another confidence level (besides 80%, 95% or 99%) to create another confidence interval.
3. Provide a sentence for each confidence interval created above which explains what the confidence interval means in context of topic of your project.
Computations
(Round all values to TWO decimal places)
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Calculate each of the following.)
Sample Mean =
Sample Standard Deviation =
80% Confidence Interval:
80% Confidence Interval Margin of Error:
Sentence:
95% Confidence Interval:
95% Confidence Interval Margin of Error:
Sentence:
99% Confidence Interval:
99% Confidence Interval Margin of Error:
Sentence:
______% Confidence Interval:
______% Confidence Interval Margin of Error:
Sentence
Problem Analysis
(REMOVE THESE LINES PRIOR TO SUBMITTING REPORT: Write a half-page reflection. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?)
Course Project, Part II
Preliminary Calculations
Round Preliminary Values to the nearest whole number.
Summary Table for:
Live Births
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Deaths
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Divorces
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Marriages
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Hypothesis Testing
With the information that you gather from the Summary Tables above, test the following (you can use excel when appropriate):
Hypothesis Test #1:
Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.
Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test.
Ho: μ ≥ ≤ =
Ha: μ < > ≠
Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test
Step 2: Determine the Rejection Region
Pick ONE multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.
a) ...
Himani
The document discusses hypothesis testing procedures. It describes the 7 steps of hypothesis testing which include setting the null and alternative hypotheses, choosing a statistical test, setting the significance level, establishing decision rules, collecting sample data, analyzing the data, and arriving at a statistical conclusion. Common statistical tests mentioned are F-tests, t-tests, and z-tests. The F-test compares variances by taking the ratio and uses sums of squares to develop statistics. The document provides an example of a company collecting potential customer spending data on flats in two areas to estimate differences in population means.
Himani sharma
The document discusses hypothesis testing procedures. It describes the 7 steps of hypothesis testing which include setting the null and alternative hypotheses, choosing a statistical test, setting the significance level, establishing decision rules, collecting sample data, analyzing the data, and arriving at a statistical conclusion. Common statistical tests mentioned are F-tests, t-tests, and z-tests. The F-test compares variances by taking the ratio and uses sums of squares to develop statistics. The document provides an example of a company collecting potential customer spending data on flats in two areas to estimate differences in population means.
STATISTIC ESTIMATION
This document provides an overview of statistical inference. It discusses descriptive statistics, which summarize data, and inferential statistics, which are used to generalize from samples to populations. Key concepts covered include estimation, hypothesis testing, parameters, statistics, confidence intervals, significance levels, types of errors. Examples are given of how to calculate confidence intervals for means and proportions and how to perform hypothesis tests using z-tests and t-tests. Steps for conducting hypothesis tests are outlined.
Hypothesis Testing Definitions A statistical hypothesi.docx
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
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Fundamentals of Testing Hypothesis
This document discusses hypothesis testing, including:
- The chapter introduces hypothesis testing and defines key concepts like the null hypothesis, alternative hypothesis, type I and type II errors, and significance levels.
- It explains how to formulate and test hypotheses about population means and proportions, including how to determine critical values and p-values.
- The steps of hypothesis testing are outlined, and an example is provided to demonstrate how to test a claim about a population mean using a z-test.
- Both critical value and p-value approaches to testing hypotheses are described.
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II. Properly conducted randomized experiments can establish causality but have limitations like cost and feasibility. Natural and quasi-experiments are alternatives but need to account for selection bias.
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Statistical Inference /Hypothesis Testing
This document discusses hypothesis testing and related statistical concepts. It begins with an outline of the key topics to be covered, including the concept of hypothesis testing, motivation for its use, null and alternative hypotheses, types of errors, and examples. It then provides more detailed explanations and examples of these topics:
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- Examples show how hypothesis testing can help decision makers determine if new suppliers or products meet claimed standards.
- The null hypothesis states there is no difference or effect, while the alternative hypothesis specifies an expected difference.
- Type I errors incorrectly reject the null hypothesis, while type
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This document discusses data analysis and hypothesis testing. It covers:
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2. The meaning and definition of a hypothesis, including the concept of a null hypothesis.
3. The key steps in hypothesis testing: formulating hypotheses, selecting a significance level, choosing a test criterion, and making a decision.
4. Types of errors in hypothesis testing, including Type I and Type II errors.
5. Examples of common parametric tests like z-tests, t-tests, and F-tests, which assume parameters exist about the population.
6. The concept of non-parametric
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Chapter 10 One sample test of hypothesis.ppt
The passage discusses the importance of copyright and how it protects original works of authorship such as books, music, art, and movies. Copyright gives the creator exclusive rights to make copies, distribute copies, make derivative works, perform publicly, and display publicly. These rights help ensure that creators can benefit financially from their works and have the incentive to create new works.
1667390753_Lind Chapter 10-14.pdf
its a reference book for your knowledgement about statistics and data analys . Its a Lind chapter10 to 14 .
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
This document outlines the steps for conducting a hypothesis test using the classical or critical value method for a one-sample case. It discusses the objectives, elements, and steps of hypothesis testing. The key elements are the null and alternative hypotheses, significance level, critical values of the test statistic, and the critical region used to determine whether to reject or fail to reject the null hypothesis. An example walks through applying the steps, which include formulating hypotheses, selecting a test statistic, establishing the critical region, computing the test statistic, and making a decision. The document emphasizes understanding hypothesis testing procedures and being able to apply the critical value method to real-life problems.
Course Project, Part IIntroduction(REMOVE THIS LINE PRIOR
Course Project, Part I
Introduction
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Summarize what you have learned about confidence intervals. Discuss why it would be important to know the population mean of the data used for this term. Is this an important health measure?)
Sample Data
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: List ALL of the sample data in the table below.)
Directions:
1. Use the table above to create an 80%, 95%, and 99% confidence interval.
2. Choose another confidence level (besides 80%, 95% or 99%) to create another confidence interval.
3. Provide a sentence for each confidence interval created above which explains what the confidence interval means in context of topic of your project.
Computations
(Round all values to TWO decimal places)
(REMOVE THIS LINE PRIOR TO SUBMITTING REPORT: Calculate each of the following.)
Sample Mean =
Sample Standard Deviation =
80% Confidence Interval:
80% Confidence Interval Margin of Error:
Sentence:
95% Confidence Interval:
95% Confidence Interval Margin of Error:
Sentence:
99% Confidence Interval:
99% Confidence Interval Margin of Error:
Sentence:
______% Confidence Interval:
______% Confidence Interval Margin of Error:
Sentence
Problem Analysis
(REMOVE THESE LINES PRIOR TO SUBMITTING REPORT: Write a half-page reflection. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?)
Course Project, Part II
Preliminary Calculations
Round Preliminary Values to the nearest whole number.
Summary Table for:
Live Births
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Deaths
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Divorces
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Summary Table for:
Marriages
Mean
Median
Sample Standard Deviation
Minimum
Maximum
Sample Size
Hypothesis Testing
With the information that you gather from the Summary Tables above, test the following (you can use excel when appropriate):
Hypothesis Test #1:
Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.
Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test.
Ho: μ ≥ ≤ =
Ha: μ < > ≠
Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test
Step 2: Determine the Rejection Region
Pick ONE multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.
a) ...
Himani
The document discusses hypothesis testing procedures. It describes the 7 steps of hypothesis testing which include setting the null and alternative hypotheses, choosing a statistical test, setting the significance level, establishing decision rules, collecting sample data, analyzing the data, and arriving at a statistical conclusion. Common statistical tests mentioned are F-tests, t-tests, and z-tests. The F-test compares variances by taking the ratio and uses sums of squares to develop statistics. The document provides an example of a company collecting potential customer spending data on flats in two areas to estimate differences in population means.
Himani sharma
The document discusses hypothesis testing procedures. It describes the 7 steps of hypothesis testing which include setting the null and alternative hypotheses, choosing a statistical test, setting the significance level, establishing decision rules, collecting sample data, analyzing the data, and arriving at a statistical conclusion. Common statistical tests mentioned are F-tests, t-tests, and z-tests. The F-test compares variances by taking the ratio and uses sums of squares to develop statistics. The document provides an example of a company collecting potential customer spending data on flats in two areas to estimate differences in population means.
STATISTIC ESTIMATION
This document provides an overview of statistical inference. It discusses descriptive statistics, which summarize data, and inferential statistics, which are used to generalize from samples to populations. Key concepts covered include estimation, hypothesis testing, parameters, statistics, confidence intervals, significance levels, types of errors. Examples are given of how to calculate confidence intervals for means and proportions and how to perform hypothesis tests using z-tests and t-tests. Steps for conducting hypothesis tests are outlined.
Hypothesis Testing Definitions A statistical hypothesi.docx
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
Random Forest Regression Analysis Reveals Impact of Variables on Target Values
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This overview discusses the predictive analytical technique known as Random Forest Regression, a method of analysis that creates a set of Decision Trees from a randomly selected subset of the training set, and aggregates by averaging values from different decision trees to decide the final target value. This technique is useful to determine which predictors have a significant impact on the target values, e.g., the impact of average rainfall, city location, parking availability, distance from hospital, and distance from shopping on the price of a house, or the impact of years of experience, position and productive hours on employee salary. Random Forest Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. Random Forest Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.Chap010.ppt
This document provides an overview of one-sample hypothesis tests. It defines key terms related to hypothesis testing such as the null and alternative hypotheses, test statistic, critical value, Type I and Type II errors, and p-value. It explains the five-step hypothesis testing procedure and how to set up hypotheses for tests involving a population mean or proportion. Examples are provided to demonstrate how to conduct hypothesis tests about a population mean when the population standard deviation is known or unknown, and how to conduct a test about a population proportion. The document also discusses how to interpret p-values and the concept of Type II errors.
Business Research Methods Unit V
This document discusses various topics related to data analysis and hypothesis testing in business research methods. It covers data processing operations like editing, coding, classification and tabulation. It also discusses various graphical representations of data like bar charts, pie charts, histograms and their appropriate usage. The document then explains the concepts of hypothesis, null hypothesis and alternative hypothesis. It describes hypothesis testing logic and the concepts of type 1 and type 2 errors. It lists the steps involved in hypothesis testing like setting up the hypothesis, determining test statistics, critical regions, and making decisions.
Fundamentals of Testing Hypothesis
This document discusses hypothesis testing, including:
- The chapter introduces hypothesis testing and defines key concepts like the null hypothesis, alternative hypothesis, type I and type II errors, and significance levels.
- It explains how to formulate and test hypotheses about population means and proportions, including how to determine critical values and p-values.
- The steps of hypothesis testing are outlined, and an example is provided to demonstrate how to test a claim about a population mean using a z-test.
- Both critical value and p-value approaches to testing hypotheses are described.
Customer retention measurement.
I. Smart experiment design is critical to draw valid conclusions about causal relationships. Experiments must be Specific, Measurable, Achievable, Relevant, and Time-bound.
II. Properly conducted randomized experiments can establish causality but have limitations like cost and feasibility. Natural and quasi-experiments are alternatives but need to account for selection bias.
III. Many ideas fail to improve metrics, so a test-and-learn approach is needed to identify the few successful initiatives. Statistical analysis helps ensure results aren't due to chance.
Statistical Inference /Hypothesis Testing
This document discusses hypothesis testing and related statistical concepts. It begins with an outline of the key topics to be covered, including the concept of hypothesis testing, motivation for its use, null and alternative hypotheses, types of errors, and examples. It then provides more detailed explanations and examples of these topics:
- Hypothesis testing involves using sample data to determine if there is evidence to reject or fail to reject claims about a population.
- Examples show how hypothesis testing can help decision makers determine if new suppliers or products meet claimed standards.
- The null hypothesis states there is no difference or effect, while the alternative hypothesis specifies an expected difference.
- Type I errors incorrectly reject the null hypothesis, while type
165662191 chapter-03-answers-1
This document provides 10 teaching suggestions for instructors to help students better understand key concepts in decision analysis. Suggestions include having students describe personal decisions they made and which steps of the decision-making process they used; role playing to define problems and alternatives; discussing decision types like certainty, risk, and uncertainty; and using decision trees to analyze large, complex problems by breaking them into smaller parts. The document also provides two alternative examples applying decision analysis concepts to a case study about a business owner deciding whether to purchase industrial robots.
165662191 chapter-03-answers-1
This document provides 10 teaching suggestions for instructors to help students better understand key concepts in decision analysis. Suggestions include having students describe personal decisions they made and which steps of the decision-making process they used; role playing to define problems and alternatives; discussing types of decisions under certainty, risk, and uncertainty; and using decision trees and Bayesian analysis to solve problems. The goal is for students to recognize how decision theory applies to important real-life decisions. Alternative examples provided apply concepts like expected monetary value to problems involving purchasing industrial robots.
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This document discusses various topics related to report writing including findings, conclusions, recommendations, types of reports, report sections, and explores common myths about reports. It provides examples of different sections within reports including an executive summary, company overview, factors for analysis and methodology. The summaries focus on conveying the high-level purpose or content of the different sections while keeping the summary brief.
UNIT 4 PPT.pptx
This document discusses data analysis and hypothesis testing. It covers:
1. The importance of properly analyzing collected data, including preparing analysis tables and frameworks before data collection.
2. The meaning and definition of a hypothesis, including the concept of a null hypothesis.
3. The key steps in hypothesis testing: formulating hypotheses, selecting a significance level, choosing a test criterion, and making a decision.
4. Types of errors in hypothesis testing, including Type I and Type II errors.
5. Examples of common parametric tests like z-tests, t-tests, and F-tests, which assume parameters exist about the population.
6. The concept of non-parametric
TWO WAY ANOVA TABLE DISCUSSION AND ITS USAGE IN SPSS DISCUSSION
This document discusses a study using two-way ANOVA to analyze the effects of place and education on product sales. It tests hypotheses about the main effects of place and education as well as their interaction. The analysis found that education had a significant main effect on sales, but place and the interaction of place and education did not have significant effects. Specifically, sales differed between postgraduate and other education levels but not between cities. All assumptions for two-way ANOVA were met.
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Hypothesis testing
- 2. Formulate Null and Alternate Hypothesis Select appropriate test Choose the level of significance Collect data and calculate the Test Statistics(TS) Determine the critical value of of the TS Determine if TS calculated falls into rejection or non rejection region Reject or do not reject Null hypothesis Draw a marketing research conclusion Procedure
- 3. A statement in which no difference or effect is expected A statement in which difference or effect is expected Null Hypothesis Alternate Hypothesis 1.Formulate Null and Alternate Hypothesis
- 4. 1. Chi square test 2. ANOVA 2. Selecting an appropriate test
- 5. 3.Choosing the level of confidence/significance If we reject the null, but the null is true, then we have made a Type I error.Also known as α error If we accept the null, but the null is false, then we have made a Type II error. Also known as β error
- 6. 4. Collect data and calculate the Test Statistics(TS) 5. Determine the critical value of of the TS 6. Determine if TS calculated falls into rejection or non rejection region 7. Reject or do not reject Null hypothesis 8. Draw a marketing research conclusion
- 7. Question 1. The marketing manager of a telecommunication is reviewing the results of a study of potential users of a new cell phone. The study used a random sample 200 respondents and was conducted in a area representative of company’s target area. The marketing manager in intrigued by one table which a cross tabulation of data on whether the target consumer would by the phone (yes or no) and or not phone has Bluetooth wireless tech. Can the marketing manager infer that an association exist between availability of blue tooth tech and buying the cell phone?
- 8. Bluetoot h feature Yes EF No EF Total Yes 80 100*100/ 200 =50 20 100*100/2 00 =50 100 No 20 100*100/ 200 =50 80 100*100/2 00 =50 100 Total 100 100 200 Would buy cell phone
- 9. Chi Square χ² = ∑(OF-EF)^2 EF EXPECTED FREQUENCY EF= (TOTAL NO IN THE ROW * TOTAL NO IN THE COLUMN) TOTAL SAMPLE SIZE • Null hypothesis =there is no association between the blue tooth tech and buying cell phone (the two variables are independent of each other) • Alternate hypothesis =there is association between the blue tooth tech and buying cell phone (the two variables are dependent of each other)
- 10. Chi Square χ² = CALCULATED 72 ASSUME SIGNIFICANCE LEVEL 0.05 FOR DOF =1 formula for dof =(n-1)*(r-1) CHI SQUARE TABULATED VALUE = 3.84 calculated TS is greater than tabulated hence we will not accept the null hyothesis means ther is a ∑(OF-EF)^2 EF