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Luden [163]
3 years ago
5

A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If th

e sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
Mathematics
1 answer:
finlep [7]3 years ago
6 0

Answer:

Th computed value of the test statistic is 3.597

Step-by-step explanation:

The null and the alternative hypothesis is as follows:

Null Hypothesis:

\mathbf{H_o:} the population correlation coefficient is equal to zero

\mathbf{H_a:} the population correlation coefficient is not equal to zero

The test statistics for Pearson correlation coefficient is thus computed as :

t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }

where;

r = correlation coefficient = 0.60

n = sample size = 25

So;

t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }

t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }

t =\dfrac{0.60 *4.796} {0.8}

t = 3.597

Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069

Decision Rule:

Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.

Conclusion:

We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.

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