Question

In a random sample of​ males, it was found that 17 write with their left hands and 208 do not. In a random sample of​ females, it was found that 57 write with their left hands and 445 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. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 B. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 C. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 D. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 E. Upper H 0​: p 1less than or equalsp 2 Upper H 1​: p 1not equalsp 2 F. Upper H 0​: p 1greater than or equalsp 2 Upper H 1​: p 1not equalsp 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 ▼ greater than less than the significance level of alphaequals0.01​, 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. b. Test the claim by constructing an appropriate confidence interval. The 98​% confidence interval is nothingless thanleft parenthesis p 1 minus p 2 right parenthesisless than nothing. ​(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 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. Click to select your answer(s).

Answer 1

P-value is greater than the significance level of alpha equals 0.01​, so fail to reject the null hypothesis.

Because the confidence interval limits include ​0, it appears that the two rates of​ left-handedness are equal..

Accept Ho

There is not sufficient evidence to support the claim that the rate of​ left-handedness among males is less than that among females