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 90​% confidence interval estimate of the population standard deviation 60 63 63 57 63 54 59 58 59 69 58 67

Answer 1

the ratio of sample variance (S2) and population variation (K2) is a chi-squared distribution.

So, if the sample size is n, the statistic (n-1)S2 / K2   has a chi-squared distribution with n-1 degrees of freedom

Proceed with finding the sample mean which comes out to be 60.83

Variance S2 = 16.972

Now, chi-squared distribution is not symmetrical like normal distribution.

90% confidence interval lies between the two black lines. Two find the chi-squared values at the two points we will divide 10% into two 5% parts.

Note : while reading a chi-squared table the values correspond to area to the right of the values.

Values of A and B can be found from chi-squared table and are B=19.67 and A=4.57

therefore, estimate for population standard deviation is

((n-1)S2 / B) < K2 < ((n-1)S2 / A)

9.49< K2<40.85

3.08 < K < 6.39