A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life.

 

Sample Size = 36 shoes

Sample Mean = 52.3 hours

Sample Standard Deviation = 9.6 hours

 

Does the sample data provide evidence to conclude that the manufacturer's claim is correct (using a = .10)? Use the hypothesis testing procedure outlined below..

 

a. Formulate the null and alternative hypotheses. 

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence to conclude that the manufacturer's claim is correct (using a = .10)? (Points : 24)