  ## Exercises - Comparing Variation

1. When testing the claim that two different samples of heights of men are from populations having the same standard deviation, a test statistic of $F = 1.010$ is obtained. What does this suggest about the sample data?

Because $F$ is so close to $1$, the two sample standard deviations are very close in value.

2. The axial load (in pounds) of a cola can is the maximum load that can be applied to the top before the can is crushed. When testing the claim that axial loads of cola cans with wall thickness of 0.0111 in. have the same standard deviation as the axial loads of cola cans with wall thickness of 0.0109 in., we find $F = 1.5777$ with an associated $p$-value of $0.0028$. At $\alpha = 0.01$ significance, what is the conclusion and inference for this test?

$H_0: \sigma_1 = \sigma_2$
$H_1: \sigma_1 \neq \sigma_2$

Conclusion: Reject the null hypothesis, as $p$-value $\lt \alpha$

Inference: There is significant evidence that the standard deviations of the axial loads are different for these two different types of cans.

3. A group of 40 subjects following the Atkins diet have a mean age of 47 with a standard deviation of 12 years. A different group of 40 subjects following the Zone diet have a mean age of 51, with a standard deviation of 9 years. Test the claim that subjects from both groups have ages with the same amount of variation. (Use $\alpha = 0.05$.)

$H_0: \sigma_1 = \sigma_2$
$H_1: \sigma_1 \neq \sigma_2$

Test statistic: $F = 1.7778$.