Question

a study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86. 1. state the decision rule for 0.05 significance level: h0: rho ≤ 0; h1: rho > 0 (round your answer to 3 decimal places.) 2. compute the value of the test statistic. (round your answer to 2 decimal places.) 3. can we conclude that the correlation in the population is greater than zero? use the 0.05 significance level.

Answer 1

The decision rule is reject H(0) if t>1.714, test statistic t is 7.157 and Yes, we can conclude that the correlation in the population is greater than zero.

In the given question,

A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86.

n=20, r = 0.86

The decision rule for α=0.05 significance level:

H(0): P ≤ 0

H(1): P > 0

Degree of freedom(df) = n-2

Degree of freedom(df) = 20-2

Degree of freedom(df) = 18

This is the right tailed test using the t table.

Critical Value: $t_{\alpha /2}$, df = $t_{\alpha /2}$ = 1.714

(a) The decision rule is reject H(0) if t>1.714.

(b) Test statistic is t

t= r√(n−2)/√(1–r^2)

t= 0.86*√(20 -2)/√(1-(0.86)^2)

t= 0.86*√18/√(1-0.7396)

t= 0.86*4.243/√0.2604

t= 3.65/0.51

t= 7.157

Test statistic = 7.157

(c)  We have to conclude that the correlation in the population is greater than zero.

Yes, we can conclude that the correlation in the population is greater than zero.

To learn more about test statistic z link is here

brainly.com/question/3006526

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