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 (more than $500) within 2 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. The numbers x₁ and x₂ of owners who report that their cars needed major repairs within the first 2 years are 53 and 78, respectively. Test the null hypothesis that no difference exists between the proportions in populations 1 and 2 needing major repairs against the alternative that a difference does exist. Use α = .10.