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 con?dence interval for the population mean?

(b) Calculate the 95% one-sample t con?dence 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?