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 98​% confidence interval estimate of the population standard deviation.

62

60

60

56

60

53

59

58

59

68

58

67

Answer 1

The standard deviation here is computed as:

X	(X - Mean(X))	(X - Mean(X))^2
62	2	4
60	60	3600
60	60	3600
56	56	3136
60	60	3600
53	53	2809
59	59	3481
58	58	3364
59	59	3481
68	68	4624
58	58	3364
67	67	4489
720		39552

The sample mean here is computed as:

The sample standard deviation now is computed here as:

Now for n - 1 = 11 degrees of freedom, we get from chi square distribution tables:

Therefore the confidence interval here is obtained as:

This is the required 98% confidence interval here.