Question

If, in a sample of n=20 selected from a normal​ population,X=60 and S=12​, what is your statistical decision if the level of​ significance,

α​, is 0.01​, 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

Solution:

Given:

n = 20

s = 12

Level of​ significance =

, the null​ hypothesis,

H₀​:μ=50, and

the alternative​ hypothesis,

H₁: μ≠50

Since H1 is not equal to type , this is two tailed test.

Part a) Determine the critical​ value(s).

df = n - 1 = 20 - 1 = 19

Level of​ significance =

Use following Excel command to get t critical values:

=T.INV.2T(probability, df)

=T.INV.2T(0.01,19)

=2.860935

=2.8609

Thus t critical values are: ( -2.8609 , 2.8609 )

Part b) Determine the test statistic, T STAT

Part c) State your statistical decision.

Since T STAT = 3.7268 > t critical values = 2.8609 , we reject null hypothesis H0. Thus we conclude that mean is different from 50.

Thus correct answer is:

D. The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ=50.