# Correlation Analysis for Given X and Y

13.7

You are given the following data for variables x aqnd y

X Y

20 16

18 12

24 18

20 17

22 21

14 10

18 10

______________________________________

a. Plot these variables in scatter-plot format. Based on this plot, what type of relationship appears to exist between the two variables?

b. Compute the correlation coefficient for these sample data. Indicate what the correlation coefficient measures.

c. Test to determine whether the population correlation coefficient is zero. Use the α = 0.05 level to conduct the test. Be sure to state the null and alternative hypotheses, and show the test statistic and decision rule clearly.

d. Refer to part c. Describe the type of hypothesis test error that could have been made.

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#### Solution Preview

See the attached Excel file.

A positive linear relationship appears to exist between the two variables i.e. as the value of x increases, the value of y increases.

b. Compute the correlation coefficient for these sample data. Indicate what the correlation coefficient measures.

Correlation coefficient 0.847065337

c. Test to ...

#### Solution Summary

Solution explains step by step method for finding correlation coefficient between X and Y. Scatter Diagram is plotted and significance test is conducted for correlation between X and Y.