Question

# Use the given degree of confidence and sample data to find a confidence interval for the...

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.

Solution :

Given that,

c = 95% = 0.95

s = 21.4

n = 27

d.f. = n - 1 = 27 - 1 = 26

= 1 - 0.95 = 0.05

/ 2 = 0.025

1 - ( / 2) = 0.975

Now , using chi square table ,

= 0.025,26 = 41.92

=  0.975,26 = 13.84

The 98% confidence interval for is,

21.4 [(27 - 1 ) / 41.92] < < 21.4[(27 - 1 ) / 13.84]

16.85 < < 29.33