Question

A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain year, monitoring the progress the students made toward completing a bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a bachelor's degree than those who immediately attended and remained at a 4-year institution. The data in the table attached below summarize the results of his study. Complete parts a) through e) below. Click here to view the sample data. Click here to view Student's t-distribution table, a) What is the response variable in this study? What is the explanatory variable? sample data O A. The response variable is the use of community college or not. The explanatory variable is the time to graduate. OB. The response variable is the time to graduate. The explanatory variable is the number of students. OC. The response variable is the time to graduate. The explanatory variable is the use of community college or not. Community No Transfer College Transfer OD. The response variable is the number of students. The explanatory variable is time to graduate 268 1141 Sample mean time to 5.37 4.39 b) Explain why this study can be analyzed using inference of two sample means. Select all that apply. graduate, in years Sample standard 1.153 1.011 A. The samples are independent. deviation time to B. The samples can be reasonably assumed to be random. graduate, in years c. The sample sizes are not more than 5% of the population. D. The population is given to be normally distributed Print Done E. The sample sizes are large (both greater than or equal to 30). n c) Does the evidence suggest that community college transfer students take longer to attain a bachelor's degree? Use an a = 0.05 level of significance. Perform a hypothesis test. Determine the null and alternative hypotheses. O A. Ho: community College <Hno transfer, Hy: Hcommunity College Hno transfer OB. Ho: community college Hno transfer, Hy: community College Hno transfer OC. Ho community College - Hno transferHy: community college Hno transfer OD. Ho: community college Hno transferH. Hcommunity College Hno transfer Determine the test statistic. t= (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) O A. The critical value is. OB. The lower critical value is The upper critical value is Should the hypothesis be rejected? the null hypothesis. The evidence V suggest that community college transfer students take longer to attain a bachelor's degree.

Answer 1

a) o The Eesponse Vezicible is the time to geaducte, The emplandtory Yazloble is the use of community College of Mot b). A}. The fomples ce independent B). The Jungle fan be {pesonably cosured to be fandom ED). The Sample fizes are lage (both gɛeater than or equal to 3o 30) 0) We wish to test Ho: Mommunity College M no Teansfer to His Mommunit College> MNo Te unstor Test statistic We have 2:001, T1 = 5:37 151 = 1.153, 1.-268, Jy = 4.34, 52 = 1.011, Ny= 1141 pooled standard deviation Op = (n-1) + (0₂1) 52² (2684) 1.183++ (1141-1)).0112 1520. 1701 1.0394 nith, 2 268 +11412 1407

5.37-4.39 1.0394 the titan 0.98 0.07056 268 Ti-XL ta 13.89 Sp H+ *** t=13.89 Since it is Eight taile test ceitical Valle = time nths thoon,2687161-2-togg, J407 = 2.239 (εiticul Valu=2.239 Since. 2.239< 13.89 se reitical Valuat Reject the null hypothesis. The evidence Support to Juggest that Community College tearsfee student take Jongeę to attain bachelog's degree

Q=0.01 d). 99% confidence in teeral for Hoppunt CalveMyaferskes us te ti-x init1,3 = , 26047141-2 to.995.1409 = 2.574 Mergin of eaque (ME) ME te op * = 25791103941 = 2.579.).0394/ mith = 0.1820 99% confidence interval is (61-62-ME , 81-84 + M:6) ( 5:37–4.39-0.1820,5-37-4.39 +0.1820) ( 0.798, 1.162) The confidence intervul is the funge from 0.798 to 1.162 fince, confidence internal contain only positive Valles Morruty lovepo Hyo Teorste > Mcommits college > MMoteurglas =1 - e) Yes , Results from past 6) and d) imply that community College cause you to take enter the to ecan a buchedos's degree

HR Console > Critical.Value=gt (0.99,1407) > Critical Value [1] 2.329001 > Teegt (0.995, 1407) > Te [1] 2.579328 >|