Question

A medical researcher surveyed 15 hospitals and found that the standard deviation for the cost for removing a person's gall bladder was $ 50. Assume that the variable is normally distributed. Based on this, what is the 90% confidence interval of the population variance?

Answer 1

Here in this scenario we have to calculate the 90% Confidence Interval for population Variance based on sample information which is ssmple Standerd deviation is s = 50 amd sample variance is s^2=250 so, to compute the 90% Confidence Interval for population Variance we need to use chi square distribution.

Further the Calculation of 90% Confidence Interval for population Variance with formula and steps as below,

We need to construct the 90\%90% confidence interval for the population variance. We have been provided with the following information about the sample variance and sample size:

Sample Variance s^2 =	250
Sample size n =	15.

The chi square critical value is calculated using chi square critical table or using Excel.

Therefore, based on the data provided, the 90\%90% confidence interval for the population variance is 147.7742<σ2<532.6733, and the 90% confidence interval for the population standard deviation is 12.1562<σ<23.0797.

Thank you.