Many dairy cows now receive injections of BST, a hormone intended to spur milk production. After the first injection, a test herd of 5151

cows increased their mean daily production from 5050

pounds to 5959

pounds of milk. The standard deviation of the increases was 6.46.4

pounds. A researcher wants to estimate the mean increase a farmer could expect from his own cows. Complete parts a) through d) below

Check the assumptions and conditions for inference. Choose the correct answer below.

A.

The assumptions and conditions appear to be satisfied. While there is no reason to believe that the differences are not independent and the sample size is large enough for the Central Limit Theorem to kick in, two different populations of cows were tested and thus the data are not paired.

B.

The assumptions and conditions appear to be satisfied. The same cows are being tested before and after injections of BST, there is no reason to believe that the differences are not independent, and the sample size is large enough for the Central Limit Theorem to kick in.

C.

The assumptions and conditions are not satisfied. While the same cows are being tested before and after injections of BST and the sample size is large enough for the Central Limit Theorem to kick in, the differences are clearly not independent.

D.

The assumptions and conditions are not satisfied. While the same cows are being tested before and after injections of BST there is no reason to believe that the differences are not independent, the sample size is not large enough for the Central Limit Theorem to kick in so we cannot assume that the differences follow a nearly Normal distribution.

b) Write a 95% confidence interval.

left parenthesis nothing comma nothing right parenthesis,

lbs

(Round to two decimal places as needed.)

c) Explain what the part b) interval means in this context.

A.

There is more than 95% confidence that the mean increase in milk production of cows after BST injection is within the confidence interval.

B.

There is 95% confidence that the mean increase in milk production of cows after BST injection is within the confidence interval.

C.

There is 95% confidence that the mean increase in milk production of cows after BST injection is less than the confidence interval's lower bound or more than its upper bound.

D.

The mean increase in milk production of cows after BST injection is within this interval 95% of the time.

d) Given the cost of BST, a farmer believes he cannot afford to use it unless he is sure of attaining at least a 2828%

increase in milk production. Based on the part b) confidence interval, what advice should he be given?

A.

He cannotcannot

justify the expense because the lower value in the confidence interval is lessless

than the amount he requires.

B.

He cancan

justify the expense because the lower value in the confidence interval is moremore

than the amount he requires