Question

Listed below are speeds (mi/h) measured from south bound traffic on I-280 near Cupertino, CA. This simple random sample was obtained at 3:30 PM on a weekday. Apply Chi-Square distribution Table A-4, or statistics technology ( calculators) to solve the following questions:

62, 61, 61, 57, 61, 54, 59, 58, 59, 69, 60, 67, 65, 64, 56 , 54

(a) Use the sample data to construct a 95% confidence interval estimate of the population variance.

(b) Use the sample data to construct a 95% confidence interval estimate of the population standard deviation.

(c) Do you think you can accept the results you got in (a) and (b)? Why or why not? (Hint: Requirements)

Answer 1

Answer:

a)

Given,

alpha = 0.05

sample n = 16

degree of freedom = n - 1 = 16 - 1 = 15

Sample variance = 18.529

95% Ci = [ ((n-1)s^2/(alpha/2 , df)) , ((n-1)s^2/(alpha/2 , df)) ]

substitute values

= [15*18.529/24.488 , 15*18.529/6.262]

= (10.11 , 44.38)

So 95% CI = 10.11 < < 44.38

b)

Here for population standard deviation

sqrt(10.11) < < sqrt(44.38)

3.18 < < 6.66

c)

If they fall in the above interval , then we accept the result or else we reject.