16.34 Using bootstrapping to check traditional methods. Bootstrapping is a good way to check if traditional inference methods are accurate for a given sample. Consider the following data:

108 107 113 104 94 100 107 98 112 97 98 95 95 97 99 95 97 90 109 102 89 101 93 95 105 91 96 104 95 87 91 101 119 116 91 95 95 104 111 101 92 91

(a) Examine the data graphically. Do they appear to violate any of the conditions needed to use the one-sample t confidence interval for the population mean?

(b) Calculate the 95% one-sample t confidence interval for this sample.

(c) Bootstrap the data, and inspect the bootstrap distribution of the mean. Does it suggest that a t interval should be reasonably accurate? Calculate the bootstrap t 95% interval.

(d) Find the 95% bootstrap percentile interval.

Does it agree with the two t intervals? What do you conclude about the accuracy of the one-sample t interval here?