Question

If another set of data gave an average of 5.045 with standard deviation of 0.098 (n=7), determine if both standard deviations are statistically different or not at 95% confidence level. First set of data: mean of 5.020, standard deviation of 0.007, and n=6.

Please explain how you got the answer I would greatly appreciate it!:)

Answer 1

Assume that the distribution of first sample is

The distribution of the second sample is and the two samples are independent.

We want to test

against

If is the sample sd for the first(second sample), the test is based on , which under the null is distributed as , where m(n) is the number of observations on the first(second) sample.

We reject the null at 5% level if or

Now observed T=(.007/.098)^2=0.005102041, m=6,n=7

Thus we reject the null at 5% significance level.