In a random sample of​ males, it was found that 27 write with their left hands and 210 do not. In a random sample of​ females, it was found that 55 write with their left hands and 454 do not. Use a 0.05 significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below.       Question content area bottom Part 1 a. Test the claim using a hypothesis test.   Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis​ test?     A. H0​: p1=p2 H1​: p1>p2   B. H0​: p1≥p2 H1​: p1≠p2   C. H0​: p1≠p2 H1​: p1=p2   D. H0​: p1=p2 H1​: p1≠p2   E. H0​: p1=p2 H1​: p1

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In a random sample of​ males, it was found that
27
write with their left hands and
210
do not. In a random sample of​ females, it was found that
55
write with their left hands and
454
do not. Use a
0.05
significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below.
 
 
 

Question content area bottom

Part 1
a. Test the claim using a hypothesis test.
 
Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis​ test?
 
 
A.
H0​:
p1=p2
H1​:
p1>p2
 
B.
H0​:
p1≥p2
H1​:
p1≠p2
 
C.
H0​:
p1≠p2
H1​:
p1=p2
 
D.
H0​:
p1=p2
H1​:
p1≠p2
 
E.
H0​:
p1=p2
H1​:
p1<p2
 
F.
H0​:
p1≤p2
H1​:
p1≠p2
Part 2
Identify the test statistic.
 
z=enter your response here
​(Round to two decimal places as​ needed.)
Part 3
Identify the​ P-value.
 
​P-value=enter your response here
​(Round to three decimal places as​ needed.)
Part 4
What is the conclusion based on the hypothesis​ test?
 
The​ P-value is
 
less than
greater than
the significance level of
α=0.05​,
so
 
reject
fail to reject
the null hypothesis. There
 
is not sufficient
is sufficient
evidence to support the claim that the rate of​ left-handedness among males is less than that among females.
Part 5
b. Test the claim by constructing an appropriate confidence interval.
 
The
90​%
confidence interval is
enter your response here<p1−p2<enter your response here.
​(Round to three decimal places as​ needed.)
Part 6
What is the conclusion based on the confidence​ interval?
 
Because the confidence interval limits
 
include only negative values,
include 0,
there
 
does not appear
appears
  
to be a significant difference between the rates of​ left-handedness among males and females. There
 
is sufficient
is not sufficient
evidence to support the claim that the rate of​ left-handedness among males is less than that among females.
Part 7
c. Based on the​ results, is the rate of​ left-handedness among males less than the rate of​ left-handedness among​ females?
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