Question

In a random sample of​ males, it was found that 26 write with their left hands and 213 do not. In a random sample of​ females, it was found that 64 write with their left hands and 464 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?

-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 or less than)the significance level of

alpha equals 0.01, so_____ (reject or fail to reject

the null hypothesis. There ____ (is or is not) 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 98% 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 ____(do not include or include 0), it appears that the two rates of​ left-handedness are ______(Equal or 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 not appear to be less than the rate of​ left-handedness among females.

C.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.

D.The results are inconclusive.

Answer 1

a)The hypotheses are

Here

The test statistic

The P-value is

The​ P-value is ___greater__(greater than or less than)the significance level of

alpha equals 0.01, so___fail to reject__ (reject or fail to reject

the null hypothesis. There __is no evidence__ (is or is not) to support the claim that the rate of​ left-handedness among males is less than that among females.

b) The confidence interval for difference in proportions is

The 98% confidence interval for difference in proportions is

Because the confidence interval limits _ include 0___(do not include or include 0), it appears that the two rates of​ left-handedness are ___equal___(Equal or not equal)

There___is not sufficient___(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) The conclusion is

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.