Question

​If, in a sample of n=30 selected from a normal​ population,X=51 and S=12​, what is your statistical decision if the level of​ significance,

α​, is 0.05​, the null​ hypothesis,H0​, is μ=50, and the alternative​ hypothesis,H1, μ≠50?

Determine the critical​ value(s).

The critical​ value(s) is(are) ____

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

Determine the test statistic, T STAT

T STAT=___

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

State your statistical decision. Choose the correct answer below.

A.
The test does not reject the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ=50.
B.
The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ=50.
C.
The test does not reject the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from μ=50.
D.
The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ=50.

Answer 1

a)

= 50, n=30, =0.05, = 51, s= 12

a)

The null and alternative hypothesis are as follows:

Ho : = 50

H1 : 50

b)

Calculate t critical value for two tailed test with df = n-1 = 30 -1 = 29

using t able we get t critical values as follows

The critical​ values are = ( -2.045 , 2.045)

c)

calculate test statistic

T STAT=  0.456

d)

since (T STAT= 0.456) > ( critical value = -2.045 ) and (T STAT= 0.456) < ( critical value = 2.045 )

we can say, Failed to reject the null hypothesis.

based on this we can say,

Do not reject the null hypothesis.

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