A feed supply company has developed a special feed supplemen

A feed supply company has developed a special feed supplement to see if it will promote weight gain in livestock. Their 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. Five staff members from the marketing department were chosen to interpret the results.

1. The interpretation by the first staff member was that 95% of the cows studied gained between 45 and 67 pounds? Is this correct? Explain any misinterpretations.

2. The interpretation by the 2nd staff member was that one can be 95% sure that a cow fed this supplement will gain between 45 and 67 pounds. Is this correct? Explain any misinterpretations.

3. The interpretation by the 3rd staff member was that one can be 95% sure that the average weight gain among cows in this study was between 45 and 67 pounds. Is this correct? Explain any misinterpretations.

4. The interpretation by the 4th staff member was that the average weight gain of cows fed this supplement will be between 45 and 67 pounds 95% of the time. Is this correct? Explain any misinterpretations.

5. The interpretation by the 5th staff member is that if this supplement is tested on another sample of cows, there is at 95% sure that their average weight gain will be between 45 and 67 pounds. Is this correct? Explain any misinterpretations.

Solution

1. The confidence interval shows average weight for population not for sample studied.

2. The confidence interval shows \"average\" weight for population not for individual unit.

3. The confidence interval shows average weight for population not for sample studied.

4. Here 95% is confidence level. not probability.

5. The confidence interval shows average weight for population not for sample studied.