Question

# Use a​ t-test to test the claim about the population mean μ at the given level...

Use a​ t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.

​Claim: μ ≠ 24​; α=0.10    Sample​ statistics: x overbar = 21.4​, s = 4.2 ​, n equals = 11

What are the null and alternative​ hypotheses? Choose the correct answer below.

A.H0​: μ≠24

Ha​: μ=24

B.H0​: μ≤24

Ha​: μ>24

C.H0​: μ=24

Ha​: μ≠24

D.H0​: μ≥24

Ha​: μ than<24

What is the value of the standardized test​ statistic?

​(Round to two decimal places as​ needed.)

What is the​ P-value of the test​ statistic?

​(Round to three decimal places as​ needed.)

Decide whether to reject or fail to reject the null hypothesis.

A. Reject H0 There is not enough evidence to support the claim.

B. Reject H0 There is enough evidence to support the claim.

C. Fail to reject H0 There is not enough evidence to support the claim.

D. Fail to reject H0 There is enough evidence to support the claim.

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 : = 24

Ha :  24

Test statistic = t

= ( - ) / s / n

= (21.4 - 24) / 42 / 11

= -2.05

df = 10

P-value = 0.0675 = 0.068 = 0.10

P-value < Reject the null hypothesis .

B. Reject H0 There is enough evidence to support the claim.

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