Elementary Statistics (12th Edition)

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

Chapter 10 - Correlation and Regression - 10-2 Correlation - Basic Skills and Concepts: 8

Answer

There is sufficient evidence to support that there is a linear correlation.

Work Step by Step

r (linear correlation coefficient) is given: r=0.7654038409. Hence the value of the test statistic: $ \frac{r}{\sqrt{(1-r^2)/(n-2)}}=\frac{0.7654038409}{\sqrt{(1-0.7654038409^2)/(16-2)}}=4.45.$ Using the table, the corresponding P value with df=16-2=14: P is less than 0.01. If the P-value is less than the significance level, then this means the rejection of the null hypothesis. Hence:P is less than 0.05, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that there is a linear correlation.
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