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

p 1 greater than p 2p1>p2.

The sample data are

x 1 equals 121x1=121​,

n 1 equals 249n1=249​,

x 2 equals 137x2=137​,

and

n 2 equals 314n2=314.

​(a) Choose the correct null and alternative hypotheses below.

A.

Upper H 0 : p 1 equals 0H0: p1=0

versus Upper H 1 : p 1 not equals 0H1: p1≠0

B.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 not equals p 2H1: p1≠p2

C.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 less than p 2H1: p1<p2

D.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 greater than p 2H1: p1>p2Your answer is correct.

​(b) Determine the test statistic.

z0equals=

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

Answer 1

Given that,

For sample 1 : x1 = 121, n1 = 249 and

For sample 2 : x2 = 137, n2 = 314 and

Pooled proportion is,

a) The null and alternative hypotheses are,

H0 : p1 = p2

H1 : p1 > p2

b) Test statistic is,

=> Test statistic = Z0 = 1.17

c) p-value = P(Z > 1.17) = 1 - P(Z < 1.17) = 1 - 0.8790 = 0.1210

=> p-value = 0.1210