Example: We are comparing the fat content of chicken eggs where the chickens have been assigned to one of two different diets. We have 12 eggs from chickens on the first diet, and 6 on the second diet. Let µ1, µ2 be the mean fat content (in g) of eggs from chickens on diets one and two (respectively). Our summary statistics: x1 = 5.5, s1 = 0.4, x2 = 6.5, s2 = 0.7 (a) What is the estimated standard error of x1 − x2? (b) If we were to perform a hypothesis test on µ1−µ2, what distribution (including degrees of freedom) would we use to calculate the p-value? (c)

Find a 95% confidence interval for µ1 − µ2. (d) Using our data as a pilot study, estimate the sample size we would need in a future study to find a 95% confidence interval for µ1−µ2 with a margin of error of 0.25. Assume that n1 = n2 in this future study.

Example: We are comparing the fat content of chicken eggs where thechickens have been assigned to one of two different diets. We have 12eggs from chickens on the first diet, and 6 on the second diet. Let #1, #2be the mean fat content (in g) of eggs from chickens on diets one andtwo (respectively). Our summary statistics: 51 = 5.5,31 = 0.4,52 = 6.5,32 = 0.7 (a) What is the estimated standard error of El — 52? (b) If we were to perform a hypothesis test on m — #2, what distribution(including degrees of freedom) would we use to calculate the p-value? (c) Create a 95% confidence interval for [1,1 — #2- (d) Using our data as a pilot study, estimate the sample size we wouldneed in a future study to create a 95% confidence interval for ”1— #2with a margin of error of 0.25. Assume that m = 112 in this future study.