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Chapter 8: Q44E (page 452)

For each of the following values of αfind the values of z for which H0:p1-p2=0would be rejected in favor of Ha:p1-p2<0.

aα=.01bα=.025cα=.05dα=.10

Short Answer

Expert verified

a. For α=.01,the value of Zis -2.326.

b. For α=.025,the value of Zis -1.96.

c. For α=.05 ,the value of Zis -1.645.

d. For α=.10,the value of Z is -1.28.

Step by step solution

01

Given information

We have to find critical values for the hypotheses

H0:p1-p2=0

And

Ha:p1-p2<0

02

Definition of Critical value

The critical value is the cut-off value for the test statistic, which decides whether to reject the null hypothesis or not.

03

Calculating Critical value

Here

α:The level of significance

α=.01

Since we have a left-tailed test (as an alternative hypothesis is left-tailed)

Using the standard normal table, the critical value at the 1% significance level for the left-tailed test is -2.326

That is

z=-2.326.

The null hypothesis will be rejected for any test statistic value less than -2.326.

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