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You draw two simple random samples from two distinct populations and calculate the following: F1 = 23.4, 51 = 4.2, n1 = 25 E2 = 25.3, 52 = 3.9, n; = 27 Using the conservative method (no pooling and no calculator or computer software), what are the degrees of freedom for this problem? What if you were to use pooling? O A. Conservative: 51;pooled:26 O B. Conservative: 50; pooled: 24 O C. Conservative: 26; pooled: 51 X G) D. Conservative: 24; pooled: 51 O E. Conservative: 24; pooled: 50 A statistics professor has been teaching first- and second-semester statistics for five years. She wants to know if the grades in her first-semester classes differ significantly from those of her second-semester classes. She takes a random sample of final grades from her two most recent first- and second-semester classes and gets these data: First semester: (89, 98, 78, 86, 95, 83, 90, 87, 85, 80, 96, 93, 90, 91, 81, 87, 93, 90, 87, 88) Second semester: (87, 85, 89, 78, 79, 77, 82, 90, 91, 93, 88, 87, 86, 83, 85, 81, 90, 86, 86, 84) Compute the statistics necessary to construct a confidence interval for the difference between these two populations. XO A. X = 88.35, s = 5.314, n = 20 O B. X = -3, s = 7.3, n = 20 O C. X = 85.35, s = 4.368, n= 20 O D. X1 = 88.35, $1 = 5.314, my= 20 X2 = 85.35, $2 = 4.368, n2 = 20 O E. X1 = 85.35, $1 = 4.368, n1 = 20 X2 = 86.85,$2 = 4.841, n2 = 40A backpack manufacturer wants to know if students in high school carry more books than college students do. Company researchers take a simple random sample from each group and record the number of textbooks each subject is carrying. They get the following data: High school: (5, 3, 2, 5, 6, 4, 7, 6, 5, 4, 3, 2, 1, 4, 3, 0, 2) College: (5, 3, 2, 4, 1, 0, 0, 3, 6, 2, 1, 3, 1, 2, 4, 4, 2) Using high-school students as sample one and college students as sample two, the researchers compute the following sample statistics and t statistic: X1 = 3.647, $1 = 1.9, my = 17 X2 = 2.529, $2 = 1.7, n2 = 17 t = 1.808 Calculate the degrees of freedom, k, using the conservative method, and use tcdf on your calculator to find the Pvalue for the hypothesis test Ho: #1 = #2, Ha: #1 > #2. A. K= 17, p= .0441 B. K= 16, p= .0447 XO C. K= 32, p= .0800 D. K= 32, p= .0400 E. K= 16, p= .0894A research firm wants to determine whether there's a difference in married couples between what the husband earns and what the wife earns. The firm takes a random sample of married couples and measures the annual salary of each husband and wife. What formula should the researchers use to find the confidence interval for the difference in means? O A. ( X 1 - X2 ) + t* s 1 + 1 12 O B. Xmanz + t* S 2 $1 -2 XO C. ( X 1 - X2) +t* + m1 n2 X1 - X2 t= O D. 2 $2 n2 OE to Xm -12 - HO SWhich of the following best describes the condition necessary to justify using a pooled estimator of the population variance? 0 A. Both sample sizes are the same. 0 B. Both populations have the same standard deviation. X G) C. Both samples have the same standard deviation. 0 D. Both samples are drawn from a normal population. 0 E. The sum of the sample sizes is greater than 40. X Incorrect