Answer to Question #273714 in Statistics and Probability for Jason

Question

15 New York Times bestselling fiction books had a standard deviation of 6.17 weeks on

the list. 16 New York Times bestselling nonfiction books had a standard deviation of

13.1 weeks. At the 10% significance level, can we conclude there is a difference in the

variance? Is there a difference between the variances of the number of weeks on the

best seller lists for nonfiction and fiction books?

Answer 1

Null and alternative hypothesis:

$\begin{aligned} &\mathrm{H}_{0}: \sigma_{1}{ }^{2}=\sigma_{2}{ }^{2} \\ &\mathrm{H}_{1}: \sigma_{1}{ }^{2} \neq \sigma_{2}{ }^{2} \end{aligned}$

Test statistic:

$\mathrm{F}=\mathrm{s}_{1}^{2} / \mathrm{s}_{2}^{2}=38.0689 / 172.1344=0.22$

Degree of freedom:

$\begin{aligned} &\mathrm{df}_{1}=n_{1}-1=14 \\ &\mathrm{df}_{2}=n_{2}-1=14 \end{aligned}$

P-value:

P-value $=2^{*} F.DIST.RT (0.2212,14,14)=1.9921$

Conclusion:

As p-value $>\alpha,$ we fail to reject the null hypothesis.

There is no difference in variances