Question

Examine the following hypothesis test with

nequals=22

x overbarxequals=71.4

sequals=9.8

and

alphaαequals=0.025

H0​: muμ	less than or equals≤	70
HA​: muμ	greater than>	70

a. State the decision rule in terms of the critical value of the test statistic.

b. State the calculated value of the test statistic.

c. State the conclusion.

a. State the decision rule. Select the correct choice below and fill in any answer boxes in your choice.

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

A.Reject the null hypothesis if the calculated value of the test​ statistic, t, is greater than the critical value of

nothing.

​Otherwise, do not reject.

B.Reject the null hypothesis if the calculated value of the test​ statistic, t, is less than the critical value of

nothing

or greater than the critical value of

nothing.

​Otherwise, do not reject.

C.Reject the null hypothesis if the calculated value of the test​ statistic, t, is less than the critical value of

nothing.

​Otherwise, do not reject.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 70

H_a : > 70

Test statistic = t

= ( - ) / s / n

= (71.4 - 70) / 9.8 / 22

= 0.67

df = 21

Critical value = 2.414

Test statistic < critical value

Fail to reject the null hypothesis .

The calculated value of the test​ statistic, t, is less than the critical value of .2.414