statistics

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

Ho:

Ha:

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