8.4. 2. In a survey of 210 males ages 20 to 24, 38% were neither in school nor working. In a survey of 220 females ages 20 to 24, 45% were neither in school nor working. These samples are random and independent. At α=0.06, can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Complete parts (a) through (e) below.
8.4. 2. In a survey of 210 males ages 20 to 24, 38% were neither in school nor working. In a survey of 220 females ages 20 to 24, 45% were neither in school nor working. These samples are random and independent. At α=0.06, can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Complete parts (a) through (e) below.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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8.4. 2. In a survey of
210
males ages 20 to 24,
38%
were neither in school nor working. In a survey of
220
females ages 20 to 24,
45%
were neither in school nor working. These samples are random and independent. At
α=0.06,
can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Complete parts (a) through (e) below.(a) Identify the claim and state
H0
and
Ha.
The claim is "the proportion of males ages 20 to 24 who were neither in school nor working is
the proportion of females ages 20 to 24 who were neither in school nor working."
(1)
Let
p1
and
p2
be the two population proportions for males and females, respectively. State
H0
and
Ha.
Choose the correct answer below.
H0:
p1=p2
Ha:
p1≠p2
H0:
p1≥p2
Ha:
p1<p2
H0:
p1<p2
Ha:
p1≥p2
H0:
p1≤p2
Ha:
p1>p2
H0:
p1≠p2
Ha:
p1=p2
H0:
p1>p2
Ha:
p1≤p2
(b) Find the critical value(s) and identify the rejection region(s).
The critical value(s) is(are)
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Identify the rejection region(s). Choose the correct answer below.
z>z0
z≥z0
z<−z0,
z>z0
z≤−z0,
z≥z0
z=z0
z<−z0
(c) Find the standardized test statistic.
z=
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Choose the correct answer below.
Fail to reject
H0.
Reject
H0.
(e) Interpret the decision in the context of the original claim.
Choose the correct answer below.
At the
6%
significance level, there is
insufficient
evidence to support the claim.At the
6%
significance level, there is
sufficient
evidence to reject the claim.At the
6%
significance level, there is
insufficient
evidence to reject the claim.At the
6%
significance level, there is
sufficient
evidence to support the claim.(1)
less than
different than
greater than
the same as
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