Question 677:

Asked on April 17, 2009

Tags: Standard Deviation , Chi-Square , sample variance , Population Standard Deviation , sampe standard deviation

1

Answer:

No answer provided yet.

If we were comparing two sample standard deviations we could use the F-test.

To compare the sample standard deviation to the population standard deviation we can use the Chi-Square test instead. 

The formula is X² = (n-1)*(s / σ) ² where n is the sample size and s is the sample standard variance and σ is the population variance. Recall that the standard deviation is the square root of the variance. We compare variances instead of standard deviations in the formula (it's the same concepts as the Pythagorean theorem). In essence we want to see if there is evidence to suggest the sample sd 6.18062 is not equal to 8. Plugging in these values gets us the test-statistic (51-1)*(6.18062/8)² = 29.84375. The question doesn't ask it, but we'd then evaluate this value using the Chi-square table on 50 degrees of freedom and we'd conclude there to be little evidence to reject Ho (p > .9).