Question: The owner of a mosquito-infested fishing camp in Alaska wants to test the effectiveness of two rival brands of mosquito repellents, X and Y. During the first month of the season, eight people are chosen at random from those guests who agree to take part in the experiment. For each of these guests, Brand X is randomly applied to one arm and Brand Y is applied to the other arm. These guests fish for 4 hours, then the owner counts the number of bites on each arm. The table below shows the number of bites on the arm with Brand X and those on the arm with Brand Y for each guest.
a. Construct a 95% confidence interval for the mean d of population paired differences, where a paired difference is defined as the number of bites on the arm with Brand X minus the number of bites on the arm with Brand Y.
b. Test at the 5% significance level whether the mean number of bites on the arm with Brand X and the mean number of bites on the arm with Brand Y are different for all such guests. Assume that the population of paired differences has a normal distribution.