Question

Consider researching the maximum distance that prospective professional quarterbacks can throw a football.  Suppose that 41 NFL draft prospect quarterbacks were asked to throw a football as far as they could.  For this sample, the mean distance was 68.9 yards and the sample standard deviation was 5.2 yards

find a 90% confidence interval for the true population standard deviation of distances

Answer 1

Solution :

Given that,

c = 0.90

s = 5.2

n = 41

At 90% confidence level the is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

/2,df = 0.05,40 = 55.76

and

1- /2,df = 0.95,40 = 26.51

2L = 2/2,df = 55.76

2R = 21 - /2,df = 26.51

The 90% confidence interval for is,

s (n-1) / /2,df < < s (n-1) / 1- /2,df

5.2 ( 41 - 1 ) / 55.76 < < 5.2 ( 41 - 1 ) / 26.51

4.40 < < 6.39

( 4.40 , 6.39)