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 plus or minus

 

±11 pounds. Five staff members from the marketing department were chosen to interpret the results. Answer parts ​(a)through ​(e).

​(a) The interpretation by the first staff member was that​ 95% of the cows studied gained between 45 and 67 pounds.

Is this interpretation​ correct? Explain any misinterpretation.

A.

The interpretation is correct.

B.

The interpretation is not correct. The confidence interval addresses the mean weight gain of the population of all​ cows, not​95% of the cows in the study.

C.

The interpretation is not correct. The confidence interval indicates that the sample of cows attained​ 95% of the desired weight gain.

​(b) The interpretation by the second staff member was that one can be​ 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.

Is this interpretation​ correct? Explain any misinterpretation.

A.

The interpretation is correct.

B.

The interpretation is not correct. The confidence interval addresses the mean weight gain of the population of all​ cows, not an individual cow.

C.

The interpretation is not correct. The confidence interval indicates that the population of​ cows, not an individual​ cow, attained​95% of the desired weight gain.

​(c) The interpretation by the third staff member was that one can be​ 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.

Is this interpretation​ correct? Explain any misinterpretation.

A.

The interpretation is correct.

B.

The interpretation is not correct. The confidence interval indicates that the population of cows attained​ 95% of the desired weight gain.

C.

The interpretation is not correct. The average weight gain of the sample was 56 pounds.

​(d) The interpretation by the fourth 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 interpretation​ correct? Explain any misinterpretation.

A.

The interpretation is correct.

B.

The interpretation is not correct. The confidence interval indicates that the population of cows maintained​ 95% of the average weight gained.

C.

The interpretation is not correct. The statement implies that the average weight gain​ varies, which it does not.

​(e) The interpretation by the fifth staff member is that 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.

Is this interpretation​ correct? Explain any misinterpretation.

A.

The interpretation is correct.

B.

The interpretation is not correct. The statement implies that there is something special about the interval. The interval could have been different depending on the cows chosen for the sample.

C.

The interpretation is not correct. The statement implies that a sample of different cows will yield the same results. It would not.st

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Status NEW Posted 13 Aug 2017 06:08 PM My Price 8.00

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