Chapter 15, Problem 1TP

1.

To determine

To test: The correlation is significant or not and verify the given statement.

Answer to Problem 1TP

There is a significant correlation between speed and strength, and the correlation accounts for 32.15% of the variance.

Explanation of Solution

Given information: The correlation between speed and strength for 20 women is 0.57.

Calculation:

The claim is:

The null hypothesis is given by;

$H_0$: There is no significant difference between speed and strength for 20 women.

The alternative hypothesis is given by;

$H_1$: There is a significant difference between speed and strength for 20 women.

The tabulated value is calculated at 1% level of significance and tail is one tailed.

The tabulated value is 0.515 and calculated or obtained value of correlation is 0.57.

Conclusion:

The calculated or obtained value of correlation is greater than tabulated value at 1% level of significance. The null hypothesis is rejected at 1% level of significance. Therefore, there is a significance difference between speed and strength for 20 women. This shows that speed of women affecting the strength of women.

2.

To determine

To test: The correlation between the number correct on a math test and the time is taken to complete the test.

Answer to Problem 1TP

There is a significant correlation between number correct and time. A one-tailed test was used because the alternative hypothesis was that the relationship was indirect or negative, and approximately 20% of the variance is accounted for

Explanation of Solution

Given information: The correlation between the number correct on a math test and the time it takes to complete the test is -.45.

Calculation:

The claim is:

The null hypothesis is given by;

$H_0$: There is no significance difference between the number correct on a math test and the time is taken to complete the test.

The alternative hypothesis is given by;

$H_1$: There is a significance difference between the number correct on a math test and the time is taken to complete the test.

The tabulated value is calculated at 5% level of significance and tail is one tailed.

The tabulated value is 0.1829 and calculated or obtained value of correlation is -0.45.

Conclusion:

The calculated or obtained value of correlation is less than tabulated value at 5% level of significance. The null hypothesis is not rejected at 5% level of significance. Therefore, there is no significance difference between the number correct on a math test and the time is taken to complete the test. This means that more number of corrections on math test needs more time.

3.

To determine

To test: The correlation between number of friends and grade point average (GPA) for 50 adolescents.

Answer to Problem 1TP

There is a significant correlation between number of friends a child might have and GPA, and the correlation accounts for 13.69% of the variance.

Explanation of Solution

Given information: The correlation between number of friends and grade point average (GPA) for 50 adolescents is .37.

Calculation:

The claim is:

The null hypothesis is given by;

$H_0$: There is no significance difference between the number of friends and grade point average (GPA) for 50 adolescents.

The alternative hypothesis is given by;

$H_1$: There is significance difference between the number of friends and grade point average (GPA) for 50 adolescents.

The tabulated value is calculated at 5% level of significance and tail is a two tailed.

The tabulated value is 0.273 and calculated or obtained value of correlation is 0.37.

Conclusion:

The calculated or obtained value of correlation is greater than tabulated value at 5% level of significance. The null hypothesis is rejected at 5% level of significance. Therefore, there is a significance difference between the number of friends and grade point average (GPA) for 50 adolescents.