Question

use the standard normal distribution or the t - distribution to construct a 95% confidence interval for the population mean. justify your decision. if neither distribution can be used, explain why. interpret the results.
in a recent season, the population standard deviation of the yards per carry for all running backs was 1.26. the yards per carry of 25 randomly selected running backs are shown below. assume the yards per carry are normally distributed.
2.5 5.8 5.7 3.7 7.4 4.8 6.3 4.5 7.2 2.3 1.4 6.4 2.9
5.7 2.9 3.6 5.2 5.3 5.6 6.2 5.4 3.6 5.4 4.7 6.1
a. the 95% confidence interval is (4.33, 5.32).
(round to two decimal places as needed.)
b. neither distribution can be used to construct the confidence interval.
interpret the results. choose the correct answer below.
a. it can be said that 95% of players have a yards per carry between the bounds of the confidence interval.
b. if a large sample of players are taken approximately 95% of them will have yards per carry between the bounds of the confidence interval.
c. with 95% confidence, it can be said that the population mean yards per carry is between the bounds of the confidence interval
d. neither distribution can be used to construct the confidence interval.

Explanation:

A confidence interval gives a range of values within which the population parameter (here, the population mean) is likely to lie. The interpretation of a confidence interval is that with a certain level of confidence (in this case, 95%), the population mean is within the calculated interval. Option A and B misinterpret the confidence interval as being about individual data points (players' yards per carry), while a confidence interval is about the population mean. Option C correctly states that with 95% confidence, the population mean yards per carry is between the bounds of the confidence interval.

Answer:

C. With 95% confidence, it can be said that the population mean yards per carry is between the bounds of the confidence interval.