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Chapter 15: Problem 43

Give the rejection region for a test to detect positive rank correlation if the number of pairs of ranks is 16 and you have these \(\alpha\) -values: a. \(\alpha=.05\) b. \(\alpha=.01\)

Short Answer

Expert verified
Answer: For 伪=.05, the rejection region is 蟻 > 0.497. For 伪=.01, the rejection region is 蟻 > 0.678.

Step by step solution

01

Understanding Spearman's rank correlation coefficient and critical values

Spearman's rank correlation coefficient (蟻) measures the degree of association between two variables, in this case, the pairs of ranks. The coefficient ranges from -1 for a perfect negative correlation to +1 for a perfect positive correlation. A coefficient near 0 indicates no correlation. The critical value of 蟻 (蟻c) is the value at which we decide to reject the null hypothesis (蟻=0).
02

Find the critical value of 蟻 for each 伪-value

- For 伪=.05, use the Spearman's rank correlation coefficient (蟻) table or online calculator to find the critical value of 蟻 (蟻c). For n=16 and 伪=.05, the critical value of 蟻 (蟻c) is approximately 0.497. - For 伪=.01, similarly, use the table or calculator to find the critical value of 蟻 (蟻c). For n=16 and 伪=.01, the critical value of 蟻 (蟻c) is approximately 0.678.
03

Determine the rejection region for each 伪-value

- For 伪=.05, the rejection region is the set of all rank correlation coefficients that are greater than the critical value 蟻c = 0.497. So, the rejection region is 蟻 > 0.497. - For 伪=.01, the rejection region is the set of all rank correlation coefficients that are greater than the critical value 蟻c = 0.678. So, the rejection region is 蟻 > 0.678.
04

Summary

For each 伪-value, we have found the corresponding critical value of 蟻 and the rejection region: a. For 伪=.05, the rejection region is 蟻 > 0.497. b. For 伪=.01, the rejection region is 蟻 > 0.678.

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