Question

Conduct a test at the

alphaαequals=0.050.05

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 2p1>p2.

The sample data are

x 1 equals 116x1=116​,

n 1 equals 243n1=243​,

x 2 equals 138x2=138​,

and

n 2 equals 303n2=303.

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

A.

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

versus Upper H 1 : p 1 greater than p 2H1: p1>p2

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 0H0: p1=0

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

​(b) Determine the test statistic.

z0equals=nothing

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

​(c) Determine the​ P-value.

The​ P-value is

nothing .

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

Answer 1

The statistical software output for this problem is:

Hence,

a) Option A is correct.

b) Test statistic = 0.51

c) P - value = 0.305