A consumer advocacy group wants to determine whether there is a (statistically significant) difference between the proportions of the two leading motorcycle models that need major repairs within 2 years of purchase. A major repair is defined as “more than $500.”
A sample of 520 owners of the Model A is contacted, and 85 owners indicated that their vehicles needed major repairs within 2 years. A sample of 610 owners of Model B is contacted, and 108 owners indicated that their vehicles needed major repairs within 2 years.
Test the null hypothesis that no difference exists between the proportions in populations A and B needing major repairs against the alternative hypothesis that a difference does exist. Use α = 0.01.
Be sure to write out the conditions for each step of the hypothesis testing procedure:
Step 1: State null and alternate hypothesis
Step 2: Select a level of significance
Step 3: Identify the test statistic
Step 4: Formulate a decision rule
Step 5: Take a sample, arrive at decision
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