Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of ± 11 pounds. Some students wrote the following conclusions. Did anyone interpret the interval correctly? Explain any misinterpretations.
a) 95% of the cows studied gained between 45 and 67 pounds.
b) We're 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.
c) We're 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.
d) The average weight gain of cows fed this supplement will be between 45 and 67 pounds 95% of the time.
e) If this supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.