Fair Market Rent. According to the document Out of Reach, published by the National Low Income Housing Coalition, the fair market rent (FMR) for a two-bedroom unit in the United States is $949. A sample of 100 randomly selected two-bedroom units yielded the data on monthly rents, in dollars, given on the WeissStats site. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean monthly rent for twobedroom units is greater than the FMR of $949? Perform the required hypothesis test both with and without the outlier.

Extending the Concepts and Skills Normal Approximation for W. The Wilcoxon signed-rank table, Table V, stops at n = 20. For larger samples, a normal approximation can be used. In fact, the normal approximation works well even for sample sizes as small as 10.

Normal Approximation for W Suppose that the variable under consideration has a symmetric distribution. Then, for samples of size n,

μW = n(n + 1)/4,

σW =

n(n + 1)(2n + 1)/24, and W is approximately normally distributed for n ≥ 10.

Thus, for samples of size 10 or more, the standardized variable z = W − n(n + 1)/4 n(n + 1)(2n + 1)/24 has approximately the standard normal distribution.