Question

Consider the hypotheses below.

H0​: μ=50

H1​: μ≠50

Given that x overbar equals x=51​,s=10​,n=25​,and alpha equals=0.05​,

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)

nothing.

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

Determine the test​ statistic,

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

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

A.

Reject the null hypothesis. The data provide

sufficient evidence to conclude that the mean differs from μ=50

B.

Do not reject the null hypothesis. The data

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

C.

Do not reject the null hypothesis. The data

provide sufficient evidence to conclude that the mean differs from

μ=50

D.

Reject the null hypothesis. The data 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.)

Click to select your answer(s).

Answer 1

Solution Given F=51,5=10 = 25 20.05 # 2/2 = 0.025 Here we want to test Ho, u 50 VS Hi: 1750 a) The critical value is naco (c. using std. Noomas Za = 20.025 = 1.960 (p 24 = 1.960) the test statistic is 22 X-1 - S1-5o = 1 = 1 / 2 = 0.50 z 515 10/525 2 = 0.50 Thus 222 1.9607 121 = 0.50 je Fail to reject Ho: u=50 at 220.05 Conclusion (B) Do not reject the null hypothesis. The data do not provide sufficient evidence to conclude that the mean differs from u=5o. IP value = 0.617 using R software > 2x proom (-abs (0.50) t] 0.61101S 20.617