Question

Age of College Students Find the 80% confidence intervals for the variance and standard deviation of the ages of seniors at Oak Park College if a random sample of 23 students has a standard deviation of 2.9 years. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round the final answers to one decimal place.

Answer 1

Solution :

Given that,

c = 0.80

s = 2.9

n = 23

At 80% confidence level the is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

/2,df = 0.10,22 = 30.81

and

1- /2,df = 0.90,22 = 14.04

Point estimate = s2 = 8.41

2L = 2/2,df = 30.81

2R = 21 - /2,df = 14.04

The 80% confidence interval for 2 is,

(n - 1)s2 / 2/2 < 2 < (n - 1)s2 / 21 - /2

( 22 *8.41) / 30.81 < 2 < ( 22 * 8.41) / 14.04

6.0 < 2 < 13.2

(6.0 , 13.2)

The 80% confidence interval for is,

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

2.9( 23 - 1 ) / 30.81 < < 2.9 ( 23 - 1 ) / 14.04

2.5 < < 3.6

( 2.5 , 3.6)