An experiment investigated weight gain in cows fed a certain livestock feed supplement. Among 77 cows that ate the supplement, weight gains averaged 25.4 kg with a standard deviation of 22.7 kg. The 95% confidence interval for the population mean weight gain was 20.3 kg to 30.5 kg.

(a) Verify that the confidence interval was calculated correctly. Note that k = tn-1 = t76= 1.99

(b) Some first-year biological science students interpreted the results as follows. In each case, indicate whether the interpretation is correct. If it is wrong, explain what is wrong with it.

(i) "95% of the cows studied gained between 20.3 kg and 30.5 kg."

(ii) "We're 95% sure that a cow fed this supplement will gain between 20.3 kg and 30.5 kg."

(iii) "We're 95% sure that the average weight gain among the cows in this study was between 20.3 kg and 30.5 kg."

(c) What is your interpretation of the confidence interval?