For Exercises 6.51 and 6.52, see pages 320–321; for 6.53 to 6.55, see pages 323–324; for 6.56 to 6.59, see pages 325–326; for 6.60 to 6.62, see pages 328–329; for 6.63 and 6.64, see page 331; and for 6.65 and 6.66, see page 332.

Question 6.53

6.53 Spending on housing.

The Census Bureau reports that households spend an average of 31% of their total spending on housing. A homebuilders association in Cleveland wonders if the national finding applies in its area. It interviews a sample of 40 households in the Cleveland metropolitan area to learn what percent of their spending goes toward housing. Take to be the mean percent of spending devoted to housing among all Cleveland households. We want to test the hypotheses

The population standard deviation is .

  1. The study finds for the 40 households in the sample. What is the value of the test statistic ? Sketch a standard Normal curve, and mark on the axis. Shade the area under the curve that represents the -value.
  2. Calculate the -value. Are you convinced that Cleveland differs from the national average?

324

6.53

(a) . (b) 0.1142. No.