A sample standard deviation for the number of passengers taking a particular airline flight is 8. A 95% confidence interval estimate of the population standard deviation is 5.86 passengers to 12.62 passengers. Was a sample size of 10 or 15 used in the statistical analysis?

Ledexadvanips

Ledexadvanips

Answered question

2022-08-10

A sample standard deviation for the number of passengers taking a particular airline flight is 8. A 95% confidence interval estimate of the population standard deviation is 5.86 passengers to 12.62 passengers. Was a sample size of 10 or 15 used in the statistical analysis?

Answer & Explanation

Franco Hickman

Franco Hickman

Beginner2022-08-11Added 11 answers

It is given that the sample standard deviation is 8. The 95% confidence interval for population standard deviation is (5.86, 12.62).
The confidence interval formula for population variance σ 2 is given below:
( n 1 ) × s 2 χ ( α / 2 ) 2 σ 2 ( n 1 ) × s 2 χ 1 ( α / 2 ) 2
The confidence interval formula for population standard deviation σ 2 is given below:
( n 1 ) × s 2 χ ( α / 2 ) 2 σ ( n 1 ) × s 2 χ 1 ( α / 2 ) 2
For n=15, the degrees of freedom is calculated as follows:
n 1 = 15 1 n = 14
Critical value for χ 1 ( α / 2 ) 2 :
χ ( 1 α / 2 ) 2 = χ ( 1 0.05 / 2 ) 2 χ 0.975 2

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