What is the conclusion based on the confidence interval?Because the confidence interval limits0, it appears that the two rates of left-handedness areThereevidence to support the claim that the rate of left-handedness among males is less than thatamong females.c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females?O A. The rate of left-handedness among males does not appear to be less than the rate of left-handedness 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 not statistically significant.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). Question HelpIn a random sample of males, it was found that 27 write with their left hands and 216 do not. In a random sample of females, it was found that 72 write with their left hands and 455 do not. Use a 0.01 significance level to test the claim that the rateof 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?B. Ho: P1 =P2O C. Ho: P1 S P2O A. Ho: P12 P2H1: P1 #P2H4: P1 # P2H1:P1 #P2O D. Ho: P1 = P2H4:P,> P2O E. Ho: P1 p2H1: P1 = P2O F. Ho: P1 = P2H1: P1

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a. Denote p1, p2 as the true population proportions of left hand male and female, respectively.It is needed to test, whether the rate of left-handedness among males is less than that among females. Null hypothesis: H0: p1 = p2. Alternative hypothesis: H1: p1 < p2. Correct option is F. It is given that, 27 males write with left hands, and 216 do not. That is, x1 = 27 and n1 = 243 (= 27 + 216). It is also given that, 72 females write with left hands, and 455 do not. That is, x2 = 72 and n2 = 527 (= 72 + 455). The sample proportions are: p̂1 ≈ 0.1111 (= 27/243). p̂2 ≈ 0.1366 (= 72/527). The pooled proportion is: p = (n1p̂1 + n2 p̂2 ) / (n1 + n2). [Here, n1 p̂1 = x1 and n2 p̂2 = x2.] = [27 + 72] / [243 + 527] ≈ 0.12857. The test statistic is: z = (p̂1 – p̂2 )/ √ [p (1 – p) (1/n1 + 1/n2)] = (0.1111 – 0.1366) / √ [(0.12857) (1 – 0.12857) (1/243 + 1/527)] = –0.0255/0.025955117 ≈ –0.98. Thus, the test statistic is –0.98. The level of significance is, α = 0.01 or 1%. Using the Excel formula =NORM.S.DIST(-0.98,TRUE) the P-value is 0.164. The decision rule regarding a hypothesis testing problem using the P-value is: If P-value ≤ α, reject the null hypothesis H0. Otherwise fail to reject H0. Since p-value (= 0.164) > α (= 0.01), fail to reject H0. The P-value is greater than the significance level α = 0.01, so fail to reject the null hypothesis. There is not enough evidence to support the claim that the rate of left handedness among males is less than among females.If 98% of the observations must lie within an interval, the remaining 2% must lie outside the interval. Further, due to symmetry, 1% will lie above the upper limit and the remaining 1% will lie below the lower limit of the interval. Thus, the upper limit of the interval is such that, 99% lie below it As a result, zα/2 = z0.01 ≈ 2.326 [Using Excel formula: =NORM.S.INV(0.99)]. Now, substitute the obtained values in the formula of confidence interval. Thus, the 90% confidence interval is –0.084 < p1 – p2 < 0.033. Because, the confidence interval limits include 0, it appears that the two rates of left handedness are equal. There is not enough evidence to support the claim that the rate of left handedness among males is less than among females. C. Based on the result, the rate of left-handedness males does not appear to be less than the rate of left-handedness among females. Correct option is A.

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EQuestion Help In a random sample of males, it was found that 27 write with their left hands and 216 do not. In a random sample of females, it was found that 72 write with their left hands and 455 do not. Use a 0.01 significance level of left-handedness among males is less than that among females. Complete parts (a) through (c) below. test the claim that the rate 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 females. What are the null and alternative hypotheses for the hypothesis test? OC. Ho: P1 SP2 O A. Ho: P, 2 P2 H: P P2 OB. Ho: P1 = P2 H P +P2 H,: P, #P2 OF. Ho: P =P2 H: P, P2 H,:P, =P2 Identify the test statistic. (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? V the null hypothesis. There V evidence to support the claim that the rate of left-handedness among males is less than that among females. The P-value is V the significance level of a = 0.01, so b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is< (P, -P2)

EQuestion Help In a random sample of males, it was found that 27 write with their left hands and 216 do not. In a random sample of females, it was found that 72 write with their left hands and 455 do not. Use a 0.01 significance level of left-handedness among males is less than that among females. Complete parts (a) through (c) below. test the claim that the rate 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 females. What are the null and alternative hypotheses for the hypothesis test? OC. Ho: P1 SP2 O A. Ho: P, 2 P2 H: P P2 OB. Ho: P1 = P2 H P +P2 H,: P, #P2 OF. Ho: P =P2 H: P, P2 H,:P, =P2 Identify the test statistic. (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? V the null hypothesis. There V evidence to support the claim that the rate of left-handedness among males is less than that among females. The P-value is V the significance level of a = 0.01, so b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is< (P, -P2)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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