2. According to the National Institute on Alcobol Abuse and Alcoholism (NIAAA), and the National Institutes ofHealth (NIH), 42% of college students nationwide engage in "binge drinking" behavior, having 5 or more drinksin one occasion during the past two weeks. A college president wonders if the proportion of students enrolled ather college that binge drink is actually different than the national proportion.In a commissioned study, 364 students are selected randomly from a list of all students enrolled at the college. Ofthese, 136 admitted to having engaged in binge drinking.Calculate the statistic for this sample.a.p-hat=136= 0.3736364b.Calculate the standard error for this sample.SE=-hat(1-p-hat)(0.3736(1-0.3736)==364SE =0.254c. Verify that we can use a normal distribution for this sample.Np-364*0.42=152.88>5ng=364*(1-0.42)=211.12>5s clear the np>5na>5 indicating that normal distribution for this sample is used.d. By hand calculate a 90% confidence interval for the proportion of all students at this college thatengage in binge drinking. Show all work. The 90% CL is 1.64CI= p-hat = z SE=0.3736+(1.645x0.0254)-0.3736+0.0418=(g.3736-0.0418,0.3736+0.0418)= (0.3318,0.4154) The 90% cl for the proportions of all students at college that engaged in binge drinkingC. Interpret the results of your confidence interval in the context of the problem.There is 90% confidence that the true proportion of all students at this college that engaged inbinge drinking lies between 0.3318 and 0.4154D. The same college president is more interested in testing her suspicion that the proportion of students at hercollege that binge drink is different than the national proportion of 37. Use the statistic provided for hercollege in problem #2 in your test.Define the null and alternative hypotheses to test this claim.a.b. By hand, calculate the test statistic for this test.Use Statkey, to perform the appropriate test and identify the resulting p-value.c.d. At a -05 significance level, what would you tell the president of the college regarding the school'sproportion of binge drinkers as compared to the national average?In order to have a margin of error of 2% with 95% confidence, what sample size would researchers havee.needed to use if they use a generic proportion of p - 0.5?

Given, Population proportion p=0.37 Sample proportion p^=0.3736 n=364 Null and alternative hypothesis: H0:p=0.37 H1:p≠0.37 Test statistic: z=p^-pp1-pn=0.3736-0.370.371-0.37364=0.1423 Thus, test statistic value is 0.1423.c) The appropriate test is one sample proportion test. Using Statkey, the p-value is obatined as follows: Thus, the p-value is 0.417+0.417 =0.834. d) Decision rule: If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: Here, p-value (0.834) is greater than the level of significance (0.05). Therefore, fail to reject the null hypothesis. At 5% level of significance the president of the college regarding the school proportion of binge drinkers is same as to the national average.e) E=0.02 confidence level = 0.95 p=0.5 critical value = 1.96 n=zα/2E2p1-p=1.960.0220.51-0.5=2401 thus, required sample size is 2401.

Math

Statistics

D. The same collge president is more interested in testing her suspicion that the proportion of students at her college that binge drink is different than the national proportion of .37. Use the statistic provided for her college in problem #2 in your test. a. Define the null and alternative hypotheses to test this elaim. b. By hand, caleulate the test statistic for this test. e. Use Statkay, to perform the appropriate test and identify the resulting p-value. d. At a -05 nignificance level, what would you tell the president of the college regarding the school's proportion of binge drinkers as compared to the national average? e. In order to have a margin of error of 2% with 95% confidence, what sample size would researchers have needed to use if they use a generic proportion of p- 0.5?

D. The same collge president is more interested in testing her suspicion that the proportion of students at her college that binge drink is different than the national proportion of .37. Use the statistic provided for her college in problem #2 in your test. a. Define the null and alternative hypotheses to test this elaim. b. By hand, caleulate the test statistic for this test. e. Use Statkay, to perform the appropriate test and identify the resulting p-value. d. At a -05 nignificance level, what would you tell the president of the college regarding the school's proportion of binge drinkers as compared to the national average? e. In order to have a margin of error of 2% with 95% confidence, what sample size would researchers have needed to use if they use a generic proportion of p- 0.5?

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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