Students were asked how many cups of coffee they typically drink in a week. The results for 15 students is in the file Coffee. Put the data into the One Mean applet using the Bootstrapping option and answer (a)–(f). 

a. What is the mean of the data? 

b. Suppose you wanted to test the hypotheses: H₀: Students drink 7 cups of coffee per week, on average (μ = 7). H_a: Students do not drink 7 cups of coffee per week, on average (μ ≠ 7). Develop a bootstrap sampling distribution for this. Give the standard deviation of the bootstrap sampling distribution and the p-value for this test. 

c. Now suppose the person that reported drinking 20 cups of coffee per week should have actually been 40 cups. Change the 20 to 40 in the dataset and redo the simulation. Give the sample mean, the standard deviation of the bootstrap sampling distribution and the p-value for this test.

d. In part (c) did your p-value increase or decrease from that in part (b)? Why did it change? 

e. Redo parts (a) through (c) but use the median as the statistic instead. Use the same 7 cups per week in the hypotheses but assume this is now a median. 

f. You should have seen that when the median is used, there really isn’t much of a change between whether the 20 cups per week is used or the 40 cups per week is used. Why don’t things change? Comment on the statistic, the standard deviation of the bootstrap sampling distribution, and the p-value.