Question: More on using bootstrapping to check traditional methods. Continue to work with the data given in Exercise.

(a) Find the bootstrap BCa or tilting 95% confidence interval.

(b) Does your opinion of the robustness of the one-sample t confidence interval change when comparing it with the BCa or tilting interval?

(c) To check the accuracy of the one-sample t confidence interval, would you generally use the bootstrap percentile or BCa (or tilting) interval? Explain.

Exercise: 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:

(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?