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:
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 ,
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