Question

1. A researcher claims that the standard deviation of the number of deaths annually from tornadoes in the US is less than 35.  If a random sample of 11 years had a standard deviation of 32, is the claim believable ?  Is this a right-tail, left-tail or a two-tail test ?   

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 35
Alternative Hypothesis, Ha: σ < 35

This is a left tailed test

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (11 - 1)*32^2/35^2
Χ^2 = 8.359

P-value Approach
P-value = 0.4062
As P-value >= 0.05, fail to reject null hypothesis.

claim is not believable