Question

Football Players:

The weights of 52 randomly selected NFL football players are presented below. The sample mean is 248.38 and the sample standard deviation is 46.68.

1. Construct a 95% confidence interval for the mean weight of NFL football players

a. Give the name of the function you would use to create the interval.

b. Give the confidence interval.

c. Interpret your interval.

305	265	287	285	290	235	300	230	195
236	244	194	190	307	218	315	265	210
194	216	255	300	315	190	185	183	313
246	212	201	308	270	241	242	306	237
315	215	200	295	187	204	257	185	255
318	230	316	200	324	245	185

Answer 1

1. a) We will use a student t distribution or t-test to calculate the confidence interval.

b) x̅ = 248.38, s = 46.68, n = 52  

95% Confidence interval :  

At α = 0.05 and df = n-1 = 51, two tailed critical value, t-crit = T.INV.2T(0.05, 51) = 2.008

Lower Bound = x̅ - t-crit*s/√n = 248.38 - 2.008 * 46.68/√52 = 235.38

Upper Bound = x̅ + t-crit*s/√n = 248.38 + 2.008 * 46.68/√52 = 261.38

c) There is 95% confidence that the population mean weight of NFL players is between 235.38 and 261.38