Question

Conduct a test at the alphaequals0.05 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 p 1 greater than p 2. The sample data are x 1 equals 126​, n 1 equals 251​, x 2 equals 137​, and n 2 equals 304. ​

​(b) Determine the test statistic. z0 equals ? ​(Round to two decimal places as​ needed.)

Answer 1

For sample 1: n1​=251, x1​=126

Sample proportion, = 126/251 = 0.502

For sample 2: n2​=304, x2​=137

Sample proportion, = 137/304 = 0.4507

The value of the pooled proportion is computed =

a) Null and Alternative Hypotheses

b) Test Statistics:

c) P-value for right tailed test using excel

=1- NORM.S.DIST(1.205,1) = 0.1141

P-value = 0.1141

As p = 0.114 >0.05, it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population proportion p1​ is greater than p2​, at the 0.05 significance level.