Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 9 - Inferences from Two Samples - 9-3 Two Means: Independent Samples - Basic Skills and Concepts - Page 466: 22


$\mu_1-\mu_2$ is between -6.3462 and 8.189, yes.

Work Step by Step

Null hypothesis:$\mu_1=\mu_2$, alternative hypothesis:$\mu_1\ne\mu_2$. The degree of freedom: $min(n_1-1,n_2-1)=min(40-1,40-1)=39.$ The corresponding critical value using the table: $t_{\alpha/2}=t_{0.025}=2.023.$ The margin of error: $E=t_{\alpha/2}\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}=2.023\sqrt{\frac{16.5201^2}{40}+\frac{15.5987^2}{40}}=7.2676.$ Hence the confidence interval $\mu_1-\mu_2$ is between $\overline{x_1}-\overline{x_2}-E$=(16.5201-15.5987)-7.2676=-6.3462 and$\overline{x_1}-\overline{x_2}+E$=(16.5201-15.5987)+7.2676=8.189. THis interval contains 0, hence there don't seem to be different sample means, hence the samples seem to originate from the same sample.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.