3. Cattle 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.

• 95% of the cows studied gained between 45 and 67 pounds.
• We’re 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.
• We’re 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.
• The average weight gain of cows fed this supplement will be between 45 and 67 pounds 95% of the time.
• 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.

4. Meal plan After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562). Now the organization is trying to write its report and is considering the following interpretations. Comment on each.

• 95% of all students pay between $1372 and $1562 for food.
• 95% of the sampled students paid between $1372 and $1562.
• We’re 95% sure that students in this sample averaged between $1372 and $1562 for food.
• 95% of all samples of students will have average food costs between $1372 and $1562.
• We’re 95% sure that the average amount all students pay is between $1372 and $1562.