In a random sample of? males, it was found that
26
write with their left hands and
214
do not. In a random sample of? females, it was found that
62
write with their left hands and
438
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.
a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of males and thesecond sample to be the sample of females. What are the null andalternative hypotheses for the hypothesis? test?
A.
Upper H 0
?:
p 1
greater than or equalsp 2
Upper H 1
?:
p 1
not equalsp 2
B.
Upper H 0
?:
p 1
not equalsp 2
Upper H 1
?:
p 1
equalsp 2
C.
Upper H 0
?:
p 1
equalsp 2
Upper H 1
?:
p 1
not equalsp 2
D.
Upper H 0
?:
p 1
equalsp 2
Upper H 1
?:
p 1
greater thanp 2
E.
Upper H 0
?:
p 1
less than or equalsp 2
Upper H 1
?:
p 1
not equalsp 2
F.
Upper H 0
?:
p 1
equalsp 2
Upper H 1
?:
p 1
less thanp 2
Identify the test statistic.
zequals
nothing
?(Round to two decimal places as? needed.)
Identify the? P-value.
?P-valueequals
nothing
?(Round to three decimal places as? needed.)
What is the conclusion based on the hypothesis? test?
The? P-value is
?
less than
greater than
the significance level of
alpha
equals0.05
?,
so
?
reject
fail to reject
the null hypothesis. There
?
is sufficient
is not sufficient
evidence to support the claim that the rate of? left-handednessamong males is less than that among females.
b. Test the claim by constructing an appropriate confidenceinterval.
The
90
?%
confidence interval is
nothing
less thanleft parenthesis p 1 minus p 2 right parenthesislessthannothing
.
?(Round to three decimal places as? needed.)
What is the conclusion based on the confidence? interval?
Because the confidence interval limits
?
do not include
include
?0, it appears that the two rates of? left-handedness are
?
not equal.
equal.
There
?
is sufficient
is not sufficient
evidence to support the claim that the rate of? left-handednessamong males is less than that among females.
c. Based on the? results, is the rate of? left-handedness amongmales less than the rate of? left-handedness among? females?
A.
The rate of? left-handedness among males
does
appear to be less than the rate of? left-handedness amongfemales because the results are statistically significant.
B.
The rate of? left-handedness among males
does
appear to be less than the rate of? left-handedness amongfemales because the results are not statistically significant.
C.
The rate of? left-handedness among males
does not
appear to be less than the rate of? left-handedness amongfemales.
D.
The results are inconclusive.
