Question

The test statistic of z = −2.21 is obtained when testing the claim that p = 3/5.

a. Using a significance level of α = 0.10, find the critical​value(s).

b. Should we reject Upper H0 or should we fail to reject Upper H0​?

a. The critical​ value(s) is/are z = ____________.

b. Choose the correct conclusion below:

A. Fail to reject H0. There is not sufficient evidence to support the claim that p = 3/5

B. Reject H0. There is not sufficient evidence to support the claim that p = 3/5

C. Fail to reject H0. There is sufficient evidence to support the claim that p = 3/5

D. Reject H0. There is sufficient evidence to support the claim that p = 3/5

(Main confusion is with a; is there a function I use in excel or a simple/easy way to do it. Sometimes I can figure this out and some I cannot). Thanks in advance

Answer 1

We are given

Ho : p = 3/5 Vs Ha : p 3/5

Test statistic Z = -2.21

a) for a = 0.10

The critical values are

Z_{​​​​​​a/2} = Z_{​​​​​​0.05} = -1.645

Z_{​​​​​​1 -a/2} = Z_{​​​​​​0.95} = 1.645

The critical values are Z = -1.645 , 1.645

b) Decision rule : If Z < Zcritical we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our Z = -2.21 < -1.645

Conclusion : Reject H0. There is sufficient evidence to support the claim that p = 3/5

Option D is correct.