Hypothesis-Testing-Single-Population

  1. State the null hypothesis, and the alternative hypothesis,
  2. Choose the level of significance, , and the sample size, n
  3. Determine the appropriate test statistic and sampling distribution
  4. Determine the critical values that divide the rejection and non-rejection regions
  5. Collect data and compute the value of the test statistic
  6. Make the statistical decision and state the managerial conclusion.
    • If the test statistic falls into the non-rejection region, do not reject the null hypothesis .
    • If the test statistic falls into the rejection region, reject the null hypothesis.
    • Express the managerial conclusion in the context of the problem

p-Value Approach to Testing

p-value: Probability of obtaining a test statistic more extreme ( or ) than the observed sample value given is true

  • Also called observed level of significance
  • Smallest value of for which can be rejected

就是把求出的值代回 求概率

If p-value , reject
If p-value , do not reject

If , then there is some evidence to reject
If , then there is strong evidence to reject
If , then there is very strong evidence to reject
If , then there is extremely strong evidence to reject

Errors in Making Decisions

Type I Error

Reject a true null hypothesis 原假设是对的却拒绝
The probability of Type I Error is

Type II Error

Fail to reject a false null hypothesis 原假设是错的却接受
Fail to reject a false null hypothesis

Type I and Type II errors cannot happen at the same time

  • Type I error can only occur if is true
  • Type II error can only occur if is false

If Type I error probability then Type II error probability
If Type I error probability then Type II error probability

Summary

Performed Z Test for the mean ( known)
Performed t Test for the mean ( unknown)
Performed Z Tests about a Population Proportion
Discussed critical value and p–value approaches to hypothesis testing
Type I & II errors

Table Of Contents
Hypothesis-Testing-Single-Population
p-Value Approach to Testing
Errors in Making Decisions
Type I Error
Type II Error
Summary