Question

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.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 24

H_a :    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.