Question 7.97

7.97 is robust.

A manufacturer of flash drives employs a market research firm to estimate retail sales of its products. Here are last month’s sales of 64GB flash drives from an SRS of 50 stores in the Midwest sales region:

retail

29	31	45	40	32	21	23	28	19	11
35	21	17	23	22	22	33	31	34	15
32	27	33	24	21	28	16	67	21	39
33	56	48	14	40	8	47	21	21	25
53	28	35	16	20	24	45	56	28	23

Make a stemplot of the data to confirm that the distribution is skewed to the right. Even though the data are not Normal, explain why the procedures can be used to analyze these data.
Let’s verify this robustness. Three bootstrap (pages 372–373) simulations, each with 1000 repetitions, give these 95% confidence intervals for mean sales in the entire region: (26.32, 33.10), (26.14, 33.22), and (26.46, 33.20). Find the 95% confidence interval for the mean. Is it essentially the same as the bootstrap intervals? Explain your answer.

7.97

(a) Because , we can use procedures for skewed data. (b) (26.06, 33.18). Yes, the interval is essentially the same as the bootstrap intervals.

29	31	45	40	32	21	23	28	19	11
35	21	17	23	22	22	33	31	34	15
32	27	33	24	21	28	16	67	21	39
33	56	48	14	40	8	47	21	21	25
53	28	35	16	20	24	45	56	28	23

29	31	45	40	32	21	23	28	19	11
35	21	17	23	22	22	33	31	34	15
32	27	33	24	21	28	16	67	21	39
33	56	48	14	40	8	47	21	21	25
53	28	35	16	20	24	45	56	28	23

29	31	45	40	32	21	23	28	19	11
35	21	17	23	22	22	33	31	34	15
32	27	33	24	21	28	16	67	21	39
33	56	48	14	40	8	47	21	21	25
53	28	35	16	20	24	45	56	28	23