Question

In a random sample of​ males, it was found that

1818

write with their left hands and

212212

do not. In a random sample of​ females, it was found that

7070

write with their left hands and

430430

do not. Use a

0.050.05

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 the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

B.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

F.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

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

▼

greater than

less than

the significance level of

alphaαequals=0.050.05​,

so

▼

reject

fail to reject

the null hypothesis. There

▼

is sufficient

is not sufficient

evidence to support the claim that the rate of​left-handedness among males is less than that among females.

b. Test the claim by constructing an appropriate confidence interval.

The

9090​%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(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

▼

equal.

not equal.

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.

c. Based on the​ results, is the rate of​ left-handedness among males less than the rate of​left-handedness among​ females?

A.The rate of​ left-handedness among males

does notdoes not

appear to be less than the rate of​left-handedness among females because the results are not statistically significant.

B.The rate of​ left-handedness among males

doesdoes

appear to be less than the rate of​left-handedness among females.

C.The rate of​ left-handedness among males

does notdoes not

appear to be less than the rate of​left-handedness among females because the results are statistically significant.

D.

The results are inconclusive.

Answer 1