Question

Find the 80% confidence interval for the standard deviation of the ages of seniors at Oak Park College if a random sample of 21 students has a standard deviation of 2.3 years. Assume the variable is normally distributed.

a.) (1.9,2.9)

b.) (2.6, 3.3)

c.) (3.7,8.5)

d.) (2.6, 7.0)

Answer 1

Solution :

Given that,

s = 2.3

s2 = 4.6

n = 21

Degrees of freedom = df = n - 1 = 21 -1 =20

At 80% confidence level the 2 value is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

1 - / 2 = 1 - 0.10= 0.90

2L = 2/2,df = 28.412

2R = 21 - /2,df = 12.4426

The 95% confidence interval for is,

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

  (20)4.6/28.412< < (20)4.6/12.4426

1.9 < < 2.9

(1.9 , 2.9)

Answer = a) ( 1.9,2.9)