Question

Listed below are speeds​ (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at​ 3:30 P.M. on a weekday. Use the sample data to construct a 980% confidence interval estimate of the population standard deviation

65
63
63
57
63   
55
61
60
61
70
62
66

The confidence interval estimate is ??? ​mi/h < σ < ??? ​mi/h.

Answer 1

Solution :

We have from data

s = 3.95

s² = 15.6

n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 98% confidence level the ² value is ,

= 0.02

/ 2 = 0.02 / 2 = 0.01

1 - / 2 = 1 - 0.01 = 0.99

²_L = ²_/2,df = 24.725

²_R = ²_{1 - /2,df} = 3.053

The 98% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

11 * 15.6 / 24.725 < < 11 * 15.6 / 3.053

2.63 mi/h < < 7.50 mi/h