Chapter 14, Problem 12P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

As we have noted in previous chapters, even a very small effect can he significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation of *r* = 0.60 for a sample of *n =* 10 participants.

**a.**Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with α = .05.**b.**If the sample had*n*= 25 participants, is the correlation significant? Again, use a two-tailed test with α = .05.

**a**.

To determine

The sample is sufficient for concluding the significant of the correlation.

Answer

The sample is not sufficient to conclude the significance of the correlation.

Explanation

**Given info:**

The correlation coefficient

**Calculation:**

The correlation coefficient is 0.60.

State the test hypotheses.

Null hypothesis:

Alternative hypothesis:

Test statistics is,

Substitute 0.60 for

For 8 degree of freedom at 5% level of significance the critical value is 2.306.

The

**Conclusion:**

The sample is not sufficient to conclude that correlation is significant.

**b**.

To determine

The sample is sufficient for concluding the significant of the correlation.

Answer

The sample is sufficient to conclude the significance of the correlation.

Explanation

**Given info:**

The correlation coefficient

**Calculation:**

The correlation coefficient is 0.60.

Set a null hypothesis

Test statistics is,

Substitute 0.60 for

For 23 degree of freedom at 5% level of significance the critical value is 2.069.

The

Thus the correlation is statistically significant.

**Conclusion:**

The sample is sufficient to conclude that correlation is significant.

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