Question

Conduct a test at the alpha α equals = 0.01 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 p1>p2. The sample data are x1=128​, n1=245​, x2=144​, and n2=315. ​(a) Choose the correct null and alternative hypotheses below.

A.

H0: p1=p2 versus H1: p1p2

B.

H0: p1=0 versus H1: p1≠0

C.

H0: p1=p2 versus H1: p1>p2 Your answer is correct.

D.

H0: p1=p2 versus H1: p1≠p2

​(b) Determine the test statistic.

z0=__?__

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

Answer 1

Answer:

Given that:

Conduct a test at the alpha α equals = 0.01 level of significance

n1 = 245

x1 = 128

n2 = 315

x2 = 144

The sample propertions are ,

p1 = x1 / n1

= 128 / 245

= 0.5224

p2=x2/n2

=144/315

=0.4571

The pooled estimate for the propertion is ,

P=(x1+x2)/(n1+n2)

=(128+144)/(245+315)

=272/560

=0.4857

Q=1-P

=1-0.4857

=0.5143

a ) The null and alternative​ hypotheses,

Hypothesis :

b ) Determine the test statistic.

The test statistic under Ho is ,