Fundamentals of Hypothesis Testing: One-Sample Tests (PPT)

Basic Business Statistics (8th Edition)
Chapter 9 - Fundamentals of Hypothesis Testing: One-Sample Tests

Chapter Topics

• 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 considerations

What is a Hypothesis?

The Null Hypothesis, H0

• Begins with the assumption that the null hypothesis is true
• Refers to the status quo
• Always contains the “=” sign
• May or may not be rejected

The Alternative Hypothesis, H1

• Is the opposite of the null hypothesis
• Challenges the status quo
• Never contains the “=” sign
• May or may not be accepted
• Is generally the hypothesis that is believed (or needed to be proven) to be true by the researcher
• Hypothesis Testing Process
• Reason for Rejecting H0
• Level of Significance,
• Defines unlikely values of sample statistic if null hypothesis is true
• Is designated by , (level of significance)
• Is selected by the researcher at the beginning
• Provides the critical value(s) of the test

Level of Significance and the Rejection Region  Errors in Making Decisions

• Type I Error
• Type II Error

Errors in Making Decisions
Probability of not making Type I Error

Called the confidence coefficient

Result Probabilities

• Type I & II Errors Have an Inverse Relationship
• Factors Affecting Type II Error

True value of population parameter
Significance level
Population standard deviation
Sample size

How to Choose between
Type I and Type II Errors


Choice depends on the cost of the errors

• Choose smaller Type I Error when the cost of rejecting the maintained hypothesis is high
• Choose larger Type I Error when you have an interest in changing the status quo

Proportion

• Involves categorical values
• Two possible outcomes
• Fraction or proportion of population in the “success” category is denoted by p

Proportion

• Sample proportion in the success category is denoted by pS
• When both np and n(1-p) are at least 5, pS can be approximated by a normal distribution with mean and standard deviation

Potential Pitfalls and Ethical Considerations

• Randomize data collection method to reduce selection biases
• Do not manipulate the treatment of human subjects without informed consent
• Do not employ “data snooping” to choose between one-tail and two-tail test, or to determine the level of significance

Potential Pitfalls and Ethical Considerations

• Do not practice “data cleansing” to hide observations that do not support a stated hypothesis
• Report all pertinent findings

Chapter Summary

• Addressed hypothesis testing methodology
• Performed Z Test for the mean ( Known)
• Discussed p –Value approach to hypothesis testing
• Made connection to confidence interval estimation

Chapter Summary

• Performed one-tail and two-tail tests
• Performed t test for the mean ( unknown)
• Performed Z test for the proportion
• Discussed potential pitfalls and ethical considerations

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