Question

Conduct a test at the

alphaαequals=0.100.10

level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling.

Test whether p1>p2.

The sample data are x1=122​, n1=252​, x2=139​, and n2=304.

B. Determine the test statistic.

z0 = ?

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

C. the critical value

D. the P- value

Answer 1

Total number of sample 1 (n1) = 252

Total number of sample 2 (n2) = 304

number of favourable events (X1) = 122

number of favourable events (X2) = 139

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.7364698957709026)

P = 0.2635

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.28   

The statistic value, 0.6325 is less than the critical values 1.28. Therefore, we fail to reject the null hypothesis.