Perform a correlation t-test to decide, at the 10% significance level, whether t

Question

Perform a correlation t-test to decide, at the 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, Upper H Subscript a Baseline : rho not equals 0 (Note: r equals negative 0.478)

x: 3, 4, 6, 5, 6

y: 3, 5, 0, -3, 2

What are the correct hypotheses for this correlation t-test?

A.Upper H 0 : rho equals 0 Upper H Subscript a Baseline : rho not equals 0

B.Upper H 0 : rho less than 0 Upper H Subscript a Baseline : rho not equals 0

C.Upper H 0 : rho greater than or equals 0 Upper H Subscript a Baseline : rho not equals 0

D.Upper H 0 : rho greater than 0 Upper H Subscript a Baseline : rho not equals 0

Compute the value of the test statistic, t.

t=?

(Round to three decimal places as needed.)

Identify the critical value(s).

The critical value(s) is(are)=

(Round to three decimal places as needed. Use a comma to separate answers as needed.)

Choose the correct conclusion below.

A.Reject Upper H 0 The data do not provide sufficient evidence to reject the null hypothesis.

B.Do not reject Upper H 0 The data provide sufficient evidence to reject the null hypothesis.

C.Do not reject Upper H 0 .The data do not provide sufficient evidence to reject the null hypothesis.

D.Reject Upper H 0. The data provide sufficient evidence to reject the null hypothesis.

Explanation / Answer

ANS option (A)

HO,RHO IS EQUAL TO ZERO

H1;RHO IS NOT ZERO

sample correlation is (r)=0.478

appropriate test statistics as t

t=r*sqrt(n-2)/sqrt(1-r^2)

=0.478*sqrt(5-2)/sqrt(1-0.478^2)

=0.9426

here t calculated is less t-tabulated (2.353)at 10% level of significance and at 5-2=3 df so we do nor reject HO

ANS ;CONCLUSION AS OPTION (c) C.Do not reject Upper H 0 .The data do not provide sufficient evidence to reject the null hypothesis

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