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.