STA 261 Chapter Notes - Chapter 8: Null Hypothesis, In Rainbows, Alternative Hypothesis
26 Jun 2018
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Module 8 - Hypothesis Testing Fundamentals (one-proportion z-tests and
one-mean t-tests) and Statistical Inference: Significance Tests About Hypotheses
● Null hypothesis, H sub 0
● Alternative hypothesis, H sub a
● Initially assume that the null hypothesis is true
● Two possible conclusions
○ Reject the null hypothesis
○ Fail to reject the null hypothesis
● Significance test for one population proportion or one-proportion z-test
○ Step #1: Assumptions
■ The variable is categorical
■ The data are obtained using randomization
■ The sample size is sufficiently large
● Np > 15 n(1-p) > 15
○ Step #2: Hypotheses
■ Null and alternative hypotheses
○ Choose a significance level for the test
○ Step #3: Compute the value of the test statistic
■ Z-stats in StatCrunch
○ Step #4: Find the p-value
■ StatCrunch
○ Step #5: State the conclusion
● Significance test for one population mean or one-mean t-test
○ Step #1: Assumptions
■ The variable is quantitative
■ The data are obtained using randomization
■ The population distribution is approximately normal or sample size is
large enough to ensure normality according to the CLT
○ Step #2: Hypotheses
■ Null and alternative hypotheses
○ Choose a significance level for the test
○ Step #3: Compute the value of the test statistic
■ T-stats in StatCrunch
○ Step #4: Find the p-value
■ StatCrunch
○ Step #5: State the conclusion
● Type I Error
○ Rejecting a true null hypothesis
■ In other words, we reject when we should not
● Type II Error
○ Failing to reject a false null hypothesis
■ In other words, we do not reject when we should
