Question

One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 18 with a sample mean of 208 pounds and a sample standard deviation of 11.1 pounds. You can assume that all of the assumptions are met.

a) What are the assumptions that are required to perform inference on this data?

b) Should you use a z distribution or a t distribution in this problem. Note that you will only get one try to get this question correct.

c) Please explain the correct answer.

d) Find the 95.9% confidence interval for the true mean weight of the players from the Detroit Red Wings.

i) If this would be a z distribution, what would be the critical value? Please use 4 decimal places.

ii) If this would be a t distribution, what would be the critical value? Please use 4 decimal places.

iii) If this would be a t distribution, what would be the degrees of freedom?

iv) The 95.9% confidence interval for the true mean weight of the players from the Detroit Red Wings is

e) Interpret your answer from the interval above (part d)

f) Please show all of the code for this part (part d) below

g) If the half-width of the interval needed to be at most 5.23 pounds, how many players would have to be randomly sampled from the team? Please use at least 4 decimal places in all numbers used (unless the number is exact). Note: This number might not be realistic. What is the new sample size?

h) Please show all of the code for this part (part g) below

Answer 1