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 H_{0} There is not enough evidence to support
the claim.

B. Reject H_{0} There is enough evidence to support the
claim.

C. Fail to reject H_{0} There is not enough evidence to
support the claim.

D. Fail to reject H_{0} There is enough evidence to
support the claim.

Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H_{0} :
= 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 .

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