a) Check the assumptions and conditions for inference. Choose the correct answer below. O A. The Paired Data Assumption and the 10% Condition are both met. There is no data with which to check the Nearly Normal Condition, but the sample size is large enough to proceed. Neither the Independence Assumption nor the Randomization Condition are met, and it is not reasonable to assume that the differences are independent or representative of all cows. OB. The Paired Data Assumption, the Independence Assumption, the Randomization Condition, and the 10% Condition are all explicitly met. There is no data with which to check the Nearly Normal Condition, but the sample size is large enough to proceed. OC. The Paired Data Assumption and the 10% Condition are both met. It is reasonable to assume that the differences are independent and representative of all cows, so the Independence Assumption and the Randomization Condition are both met. There is no data with which to check the Nearly Normal Condition, but the sample size is large enough to proceed. b) Write a 95% confidence interval. ( (Round to two decimal places as needed.) c) Explain what your interval means in this context. Choose the correct answer below. O A. For all samples, 95% of them will have a mean increase in daily milk production (in kg) after a BST injection that falls within the interval. O B. We are 95% confident that the mean increase in daily milk production (in kg) for all cows after a BST injection is between the confidence interval values. OC. Any cow has an increase in daily milk production (in kg) after a BST injection that will fall within this interval 95% of the time. O D. The confidence interval contains the mean increase in daily milk production (in kg) for all cows after a BST injection, on average, 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 27% increase in milk production. Based on your confidence interval, what advice would you give him? O A. He can justify the expense because the middle value of the confidence interval is more than the amount he requires. OB. He cannot justify the expense because the lower limit of the confidence interval is less than the amount he requires. O C. He cannot justify the expense because the lower limit of the confidence interval is more than the amount he requires. O D. He can justify the expense because the lower limit of the confidence interval is less than the amount he requires. O E. He can justify the expense because the lower limit of the confidence interval is more than the amount he requires.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...