Question

Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a population standard deviation of 47 pounds. Suppose we take a sample of 30 new players and we find that the average weight from that sample is 237 pounds. We are interested in seeing if the weight of NFL players is decreasing

1. What is the standard error?
2. What is the margin of error at 90% confidence?
3. Using my sample of 30, what would be the 90% confidence interval for the population mean?

Answer 1

Given that  NFL players weigh   = 247 pounds with a population standard deviation of s = 47 pounds. with given sample size, n=30 and sample mean M = 237.

a)  The standard error is calculated as:

b) With given population standard deviation the Margin of error is calculated using Z score for standard normal distribution which is calculated using excel formula for normal distribution at 90% confidence level.

The formula used is =NORM.S.INV(0.95) this results in Z score as 1.645

The margin of error is calculated as:

E = Zc * SE

=> E = 1.645 * 8.581

=> E = 14.1157.

c 0 The Confidence interval at 90% confidence level is caluclated as:

C I = M +/- E

so, the CI = {222.8843, 251.1157}