Consider again the weight gain data from the previous exercise.
a. Use the method of Section 8.4 to obtain a 95% confidence interval for σ. Discuss normality for the weight gain data: do you have reason to be concerned about the validity of this CI?
b. Use software to generate a bootstrap distribution of standard deviations. (That is, generate many resamples from the given data, and for each one compute the sample standard deviation s_i*)
c. Use the bootstrap standard deviation for part (a) to get a 95% bootstrap t confidence interval for σ.
d. Investigate the distribution of the bootstrap standard deviations and discuss the validity of part (c).
e. Use part (b) to form the 95% confidence bootstrap percentile interval for σ.

Data From previous exercise

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25 35 38 43 15 7 35 Here are 68 weight gains (lb) for pregnant women from conception to delivery ("Classifying Data Displays with an Assessment of Displays Found in Popular Software," Teach. Statist., Autumn 2002: 96-101). A 95% CI for the population mean weight gain u is desired. 14 24 31 28 25 32 23 30 20 21 11 35 42 31 38 21 76 22 26 31 34 36 35 33 32 25 27 31 14 -14 65 40 35 45 20 38 21 22 36 38 35 37 39 26 25 59 10 19 24 44 25 27 23 25 25 35 43 47 16 25 24