A consumer advocacy group wants to determine whether there is a difference between the proportions of the two leading automobile models that need major repairs within two years of their purchase. A sample of 400 two-year owners of model 1 is contacted and a sample of 500 two-year owners of model 2 is contacted. 53 owners of model 1 reported that their cars needed major repairs, while 78 owners of module 2 reported that their cars needed major repairs.

Required:

a.Assuming that you want to be 90% confident of your result, test the null hypothesis that no difference exists between the proportions in populations 1 and 2, against the alternative that a difference does exist and interpret your result.

b.Construct a 95% confidence interval for the difference in the population proportions. Interpret your result.