An environmental scientist is catching fish from the Great Lakes and testing them for the presence of an invasive parasite. After a sample analysis that included 175 rounds of testing, the scientist finds that the sample mean infection rate, u is 54.37 fish per round and the sample standard deviation, q, is 7.07 fish per round.

a. Construct a 95% confidence interval for the mean infection rate in the total fish population. Explain what this figure means.

b. Explain how your work in part would have been different if the sample size had been only 12 rounds of testing of 175.