Referring again to Example D in Section 7.3.3, suppose that a survey is done of another condominium project of 12,000 units. The sample size is 200, and the proportion planning to sell in this sample is .18.
a What is the standard error of this estimate? Give a 90% confidence interval.
b Suppose we use the notation P1= .12 and P2= .18 to refer to the proportions in the two samples. Let d = P1 – P2 be an estimate of the difference, d, of the two population proportions p1 and p2. Using the fact that P1 and P2are independent random variables, find expressions for the variance and standard error of.
c Since P1 and P2 are approximately normally distributed, so is d. Use this fact to construct 99%, 95%, and 90% confidence intervals for d. Is there clear evidence that p1 is really different than p2?