   Chapter 14.4, Problem 1LC Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher obtains a correlation of r = 0.39 for a sample of n 25 individuals. Does this sample provide sufficient evidence to conclude that there is a significant, nonzero correlation in the population? Assume a two-tailed test with α =.05.

To determine
If there is sufficient evidence to conclude that there is non-zero correlation in the population.

Explanation

Given info:

The Correlation for a sample of size n=25 is r=0.39 and the test is two tailed test with α=0.05.

Calculation:

The null and alternative hypotheses:

The null hypothesis:

H0:δ=0

The alternative hypothesis:

H1:δ0

The test statistic for Pearson correlation coefficient is,

t=rδ(1r2)n2

Here, α=0.05, n=25 and r=0.39.

Thus, the test statistic,

t=rδ(1r2)n2=0

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