Question

6) In a random sample of​ males, it was found that 25 write with their left hands and 209 do not. In a random sample of​ females, it was found that 75 write with their left hands and 454 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.

a1) 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?

a2) Identify the test statistic (Round to two decimal places as needed)

a3) Identify the P Value (Round to three decimal places as needed)

a4) What is the conclusion based on the hypothesis?

The P-Value is _____(greater than/less than) the significance level of alpha = 0.01, so _______(fail to reject/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.

b1) Test the claim by constructing an appropriate confidence interval.

The 98% confidence interval is ____ < (p1-p2) < ____ (Round to three decimal places as needed)

b2) What is the conclusion based on the confidence interval?

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

c1) 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 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

in sample 1 for males , we have that the sample size is n₁​=234, the number of favorable cases is x₁=25, so then the sample proportion is =x₁/n₁​​=25/234​=0.1068

in sample 2 for females , we have that the sample size is n_2​=529, the number of favorable cases is x₂=75, so then the sample proportion is =x₁/n₁​​=75/529​=01418

The value of the pooled proportion is computed as = 0.1311

the given significance level is α=0.01.

a1)

a2) the test statistic (z) = = -1.32

a3) The p-value is p = 0.094

a4) The P-Value is greater than the significance level of alpha = 0.01, so fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females.

b1) The 98% confidence interval is −0.094<p1​−p2​<0.024.

b2)Because the confidence interval limits include 0, it appears that the two rates of left-handedness are equal. There is not sufficient evidence to support the claim that the rate of left handedness among males is less than that among females.

c1 ) b) The rate of left handedness among males does appear to be less than the rate rate of left handedness among females because the results are statistically significant