Chapter 15.1, Problem 7E

Use the large-sample version of the Wilcoxon test at significance level .05 on the data of Exercise 37 in Section 9.3 to decide whether the true mean difference between outdoor and indoor concentrations exceeds .20.

37. Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concern in a number of different locales. The article “Airborne Hexavalent Chromium in Southwestern Ontario” (J. of Air and Waste Mgmnt. Assoc., 1997: 905–910) gave the accompanying data on both indoor and outdoor concentration (nanograms/m³) for a sample of houses selected from a certain region.

	House
	1	2	3	4	5	6	7	8	9
Indoor	.07	.08	.09	.12	.12	.12	.13	.14	.15
Outdoor	.29	.68	.47	.54	.97	.35	.49	.84	.86

	House
	10	11	12	13	14	15	16	17
Indoor	.15	.17	.17	.18	.18	.18	.18	.19
Outdoor	.28	.32	.32	1.55	.66	.29	.21	1.02

	House
	18	19	20	21	22	23	24	25
Indoor	.20	.22	.22	.23	.23	.25	.26	28
Outdoor	1.59	.90	.52	.12	.54	.88	.49	1.24

	House
	26	27	28	29	30	31	32	33
Indoor	.28	.29	.34	.39	.40	.45	.54	.62
Outdoor	.48	.27	.37	1.26	.70	.76	.99	.36

1. a. Calculate a confidence interval for the population mean difference between indoor and outdoor concentrations using a confidence level of 95%, and interpret the resulting interval.
2. b. If a 34th house were to be randomly selected from the population, between what values would you predict the difference in concentrations to lie?