Question

9. In a random sample of​ males, it was found that 25 write with their left hands and 223 do not. In a random sample of​ females, it was found that 74 write with their left hands and 436 do not. Use a 0.01 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.H 0​: p 1 ≤ p 2

H 1​: p 1 ≠ p 2

B.H 0​: p 1 = p 2

H 1​: p 1 > p 2

C. H 0​: p 1 = p 2

H 1​: p 1 < p 2

D. H 0​: p 1 = p 2

H 1​: p 1 ≠ p 2

E. H 0​: p 1 ≠ p 2

H 1​: p 1 = p 2

F.H 0​: p 1 ≥ p 2

H 1​: p 1 ≠ p 2

Identify the test statistic.

Z=___

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=____

​(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 alphaequals0.05​, 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.

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

The 90​% confidence interval is ___<(p1-p2),\<___

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits (include/do not 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 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 does appear to be less than the rate of​ left-handedness among females because the results are statistically significant.

C.The rate of​ left-handedness among males does not appear to be less than the rate of​ left-handedness among females.

D.The results are inconclusive.

Answer 1

T0 Test -

C.

H 0​: p 1 = p 2

H 1​: p 1 < p 2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 25 + 74 ) / ( 248 + 510 )
= 0.1306

Z = -1.70

P value = P ( Z < -1.7 )
P value = 0.0446   0.045

The​ P-value is (less than) the significance level of alpha equals 0.05​, so (reject) the null hypothesis. There (is sufficient) evidence to support the claim that the rate of​ left-handedness among males is less than that among females.

n1 = 248
n2 = 510


Lower Limit =
upper Limit =
90% Confidence interval is ( 0.004 , 0.085 )
( 0.004 < ( P2 - P1 ) < 0.085 )

Because the confidence interval limits (do not include) ​0, it appears that the two rates of​ left-handedness are (not equal). There (is sufficient) evidence to support the claim that the rate of​ left-handedness among males is less than that among females.

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