Question

# Conduct the following test at the α=0.05 level of significance by determining ​(a) the null and...

Conduct the following test at the α=0.05 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 p1≠p2. Sample data are x1=30​, n1=254​, x2=38​, and n2=302.

A. Determine the null and alternative hypotheses. Correct the answer below:

A. H0: p1 = p2 versus H1: p1≠p2

B.H0: p1=0 versus H1: p1=0

C.H0: p1=p2 versus H1: p1<p2

D.H0: p1= p2 versus H1 p1 > p2

​(b) The test statistic z0 is_____. ​(Round to two decimal places as​ needed.)

​(c) The​ P-value is____. ​(Round to three decimal places as​ needed.)

Test the null hypothesis. Choose the correct conclusion below.

A.Reject the null hypothesis because there is not sufficient evidence to conclude that p1<p2.

B.Reject the null hypothesis because there is sufficient evidence to conclude that p1≠p2.

C.Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1≠p2.

D.Do not reject the null hypothesis because there is sufficient evidence to conclude that p1>p2.

Use TI-84 calculator

press STAT then TESTS then 2-PropZTest

enter the data

x1=30

n1= 254

x2 =38

n2 =302

p1 p2

press Enter

we get

z = -0.28

p value = 0.779

(A) given that we have to test for p1 p2

So,

Option A

(B) z value = -0.28

(c) p value = 0.779

p value is greater than significance level of 0.05, failing to reject null hypothesis

therefore, we can say there is insufficient evidence to conclude that there is any significant difference

option C

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