A consumer advocacy group wants to determine whether there is a difference between

A consumer advocacy group wants to determine whether there is a difference between proportions of the two leading automobile models that need major repairs within 2 years of 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. The numbers X1 and X2 of owners who report that their cars needed major repairs within the first two years are 53 and 78, respectively. Test the null hypothesis that no difference exists between the proportions in population 1 and 2 needing major repairs against the alternative that a difference does exist. Use α = 0.10