# One-tailed test interpretations for three scenarios

Use the attached table to determine whether the correlations are significant and how you would interpret the results.

a. The correlation between speed and strength for 20 women is 0.567. Test these results at the 0.01 level using a one-tailed test.

b. The correlation between the number correct on a math test and the time it takes to complete the test is -0.45. Test whether this correlation is significant for 80 children at the 0.05 level of significance. Choose either a one-or two-tailed test and justify your choice.

c. The correlation between number of friends and grade point average (GPA) for 50 adolescents is 0.37. Is this significant at the 0.05 level for a two-tailed test?

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#### Solution Preview

a. The correlation between speed and strength for 20 women is 0.567. Test these results at the 0.01 level using a one-tailed test.

Null hypothesis: r = 0

Alternative hypothesis: r > 0

This is one tailed t test.

The degree of freedom is 18(20-2 = 18),

At 0.01 significance level, the critical t value is 2.55.

Test value t = r*sqrt((n-2)/(1-r^2)) = 0.567*sqrt((20-2)/(1-0.567^2)) = 2.92

Since 2.92 > 2.55, we could reject null hypothesis.

Based on the test, we could ...

#### Solution Summary

One-tailed test interpretations for three scenarios are examined. The correlation between speed and strengths are determined.