Question: 7.5 In a simple random sample of 200 recent purchasers of a new Make A automobile, 120 said that they were satisfied with post-purchase service. In an independent simple random sample of 250 recent purchasers of a new Make B automobile, 180 said that they were satisfied with post-purchase service. If the proportion of satisfied purchasers is actually 0.70 in both populations, what is the probability of observing a difference \({{\hat{p}}_{B}}-{{\hat{p}}_{A}}\) as large as or larger than that obtained in these surveys?