A sociologist develops a test to measure attitude about publ

A sociologist develops a test to measure attitude 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 90% confidence interval for the standard deviation, of the scores of all subjects.

a) write a brief statement that correctly interprets the confidence interval obtained in problem above.

Solution

a)
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=76.2
Standard deviation( sd )=21.4
Sample Size(n)=27
Confidence Interval = [ 76.2 ± t a/2 ( 21.4/ Sqrt ( 27) ) ]
= [ 76.2 - 1.7056 * (4.118) , 76.2 + 1.7056 * (4.118) ]
= [ 69.176,83.224 ]
b)
at 90% confidence level value of meanlies in the interval calculated