Question

Conduct the following test at the

alphaαequals=0.010.01

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

p 1 not equals p 2p1≠p2.

Sample data are

x 1 equals 30x1=30​,

n 1 equals 254n1=254​,

x 2 equals 38x2=38​,

and

n 2 equals 302n2=302.

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

A.

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

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

B.

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

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

C.

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

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

D.

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

versus Upper H 1 : p 1 equals 0H1: p1=0​(b) The test statistic

z 0z0

is

nothing.

​(Round to two decimal places as​ needed.)​(c) The​ P-value is

nothing.

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

Test the null hypothesis. Choose the correct conclusion below.

A.Do not reject the null hypothesis because there is not sufficient evidence to conclude that

p 1 not equals p 2p1≠p2.

B.Reject the null hypothesis because there is not sufficient evidence to conclude that

p 1 less than p 2p1<p2.

C.Reject the null hypothesis because there is sufficient evidence to conclude that

p 1 not equals p 2p1≠p2.

D.Do not reject the null hypothesis because there is sufficient evidence to conclude that

p 1 greater than p 2p1>p2.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option A is correct.

Test statistic = -0.28

P - value = 0.78

Conclusion: Option A is correct.