Question

1. 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. If I wanted to control my margin of error and set it to 5 at 90% confidence, what sample size would I need to take instead of the 30?
2. What are the null and alternative hypotheses?
3. What is the critical value at 90% confidence?
4. Calculate the test statistic (using the sample of 30 and NOT the answer from part a).

Answer 1

a)

Sample size = (Z/2 * / E)²

= ( 1.6449 * 47 / 5 )²

= 239.08

Sample size = 240 (Rounded up to nearest integer)

b)

The null and alternative hypothesis are

H0: >= 247

Ha: < 247

c)

From Z table,

Critical value Z/2 = Z_0.10/2 = Z_0.05 = 1.6449

d)

Test statistics

z = ( - ) / ( / sqrt (n) )

= ( 237 - 247 ) / (47 / sqrt ( 30) )

= -1.17