Question

# Consider the hypotheses below. H0​:μ=50 H1​:μ≠50 Given that x=52​, s=8​, n=20​, and α=0.10​, answer the questions...

Consider the hypotheses below.

H0​:μ=50

H1​:μ≠50 Given that x=52​, s=8​, n=20​, and α=0.10​, answer the questions below.

a. What conclusion should be​ drawn?

b. Use technology to determine the​ p-value for this test.

a. Determine 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.)

Determine the test​ statistic, t-x= Round to two decimal places as​ needed.)

What conclusion should be​ drawn? Choose the correct answer below.

A. Do not reject Do not reject the null hypothesis. The data provide provide sufficient evidence to conclude that the mean differs from μ = 50

B. Reject Reject the null hypothesis. The data provide provide sufficient evidence to conclude that the mean differs from μ=50

C. Reject Reject the null hypothesis. The data do not provide do not provide sufficient evidence to conclude that the mean differs from μ=50.

D. Do not reject Do not reject the null hypothesis. The data do not provide do not provide sufficient evidence to conclude that the mean differs from μ=50

b. Use technology to determine the​ p-value for this test. What is the​ p-value? ​p-value= ​(Round to three decimal places as​ needed.) .

Solution :

= 50

=52​

s = 8

n = 20

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 50

Ha :     50

Test statistic = t

= ( - ) / s / n

= (52​-50) / 8 / 20

= 1.118

Test statistic = t = 1.118

P-value =0.277

= 0.10

P-value ≥

0.277 ≥ 0.10

Do not reject Do not reject the null hypothesis

The data do not provide do not provide sufficient evidence to conclude that the mean differs from μ=50