Two tailed test

Question

a researcher claims that the standard deviation of the number of deaths annually from tornados in the US is less than 35. If a random sample of 11 years had a standard deviation of 32, is the claim believable? Use a=.05

Answer 1

Recall that (n-1)s²/σ² ~ χ² with n-1 degrees of freedom. This actually calls for a left-tailed test, since H_A states that σ < 35.

 

The test statistic is

 

χ² = 10·32²/35² = 8.359...

 

Using the χ² table with df = 10 shows that the p-value is between 0.1 and 0.9 (this range may differ depending on the percentiles listed in the table in your book).

 

Or you can use software (e.g. in R, calling pchisq(8.359,df=10) ) to get that the p-value is 0.4061854...

 

Thus we can't reject H₀ and the claim is not believable.