51. Here are 68 weight gains in pounds for pregnant women from conception to delivery ( Classifying Data Displays with anAssessment of DisplaysFound in Popular Software, Teaching Statist., Autumn 2002: 96—101).

25 14 20 38 21 22 36 38 35 37 35 24 31 28 25 32 23 30 39 26 38 20 21 11 35 42 31 25 59 23 43 38 21 76 22 26 10 19 25 25 15 31 34 36 35 33 24 44 35 43 7 32 25 27 31 14 25 16 25 47 35 14 65 40 35 45 27 24 We would like to get a 95% con dence interval for the population mean.

a. Compute the t-based con dence interval of Section 8.3.

b. Check for normality to see if part

(a) is valid. Is the sample large enough that the interval might be valid anyway?

c. Generate a bootstrap sample of 1000 means.

d. Use the standard deviation for part

(c) to get a 95% con dence interval for the population mean.

e. Investigate the distribution of the bootstrap means to see if part

(d) is valid.

f. Use part

(c) to form the 95% con dence interval using the percentile method.

g. Compare the intervals. If they are all close, then the bootstrap supports the use of part (a).