Advanced Business Statistics Assortment of Questions with Answers

Advanced Business Statistics Question 1 Correct Marked out of 1 A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If What is the decision if we use 1% level of significance? Select one: a. Fail to reject the null hypothesis and conclude the means are different. b. Reject the null hypothesis and conclude the means are different. c. Fail to reject the null hypothesis and conclude the means are the same. d. Reject the null hypothesis and conclude the means are the same. H0: µ A = µB H:µ ≠µ 1 A B Decision rule: reject Ho if calculated t > 2.797 or t < -2.797 (t, two-tailed test, a = 0.01, df = 12+14-2 = 24) 2 2 pooled variance =[(12-1)*1.0 + (14-1)*0.5 ]/(12+14-2) = 0.5938 t = (2.0-3.0)/sqrt(0.5938(1/12 + 1/14)) = -3.299 or t = (3-2)/sqrt(0.5938(1/12 + 1/14)) = 3.299 The computed test statistic of 3.299 or -3.299 falls within the rejection area, so we reject the null hypothesis and conclude there is a difference in the average errors of the two processes. The correct answer is: Reject the null hypothesis and conclude the means are different.  Question 2 Correct Marked out of 1 Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the: Select one: a. t distribution with df = 80. b. t distribution with df = 41. c. t distribution with df = 82. d. t distribution with df = 81. Your answer is correct. Since variances are unknown, use the t distribution with degrees of freedom (37 + 45) - 2 = 80. The correct answer is: t distribution with df = 80. Question 3 Correct Marked out of 1 A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The researcher is interested in determining whether there is evidence that Process B yields higher average errors than Process A. The population standard deviations are unknown but assumed equal. What is the critical value at the .05 level of significance? The results are presented next. Sample mean Process A Process B 3 4 Sample standard deviation 1 Sample size 13 0.5 15 Select one: a. 1.703 b. 2.052 c. 2.056 d. 1.701 e. 1.706 Your answer is correct. given the claim keyword "higher average errors", the null hypothesis H0: µB ≤ µA , clearly a one-tailed t test. The population standard deviations are unknown but assumed equal, the associated degrees of freedom for this t-statistic is: 13 + 15 - 2 = 26 Go to the t table, go down the left-hand column to 26 degrees of freedom, move across that row to the column labeled: one-tailed test at the .05 significance level. The value is 1.706. The correct answer is: 1.706  Question 4 Correct A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Marked out of 1 Sample Size Sample Mean Population Standard Deviation Men Women 25 30 25 28 5 10 At the .01 significance level, can we claim whether there is a difference in the saving between women and men? Select one: a. Fail to reject the Ho. We cannot claim that there is no difference in the saving between women and men. b. Reject the Ho. We cannot claim that there is no difference in the saving between women and men. c. Reject the Ho. We can claim that there is no difference in the saving between women and men. d. Fail to reject the Ho. We can claim that there is no difference in the saving between women and men. Your answer is correct. We know population standard deviations, two-sample z test of means is needed. H0: μ w = μ m H1: μ w ≠ μ m Decision rule: reject H if z > 2.58 or Z < -2.58 (two-tailed z test, 0.5 - a/2 = 0.5 - 0.01/2 = 0 0.4950 the area, corresponding to z = 2.58) 2 2 z = (28 - 25)/sqrt(10 /30 + 5 /25) = 3/2.08 = 1.44 Since calculated z does not fall within the rejection area, we fail to reject the H . o We can claim that there is no difference in the saving between women and men. The correct answer is: Fail to reject the Ho. We can claim that there is no difference in the saving between women and men.  Question 5 Correct Marked out of 1 Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal. Select one: a. 25 b. 28 c. 13 d. 26 e. 27 Population standard deviations are equal => df = n1 + n2 - 2 = 14 + 13 - 2 = 25 The correct answer is: 25  Question 6 Correct A telecommunications analyst is interested in knowing if there is a significant difference in the average quality of service (QQS) between cable television subscribers and satellite television Marked out of 1 subscribers. She randomly selects 50 cable subscribers and 50 satellite subscribers for the study. She gives each subscribers a survey and asks them to complete it. She tallies the results of the survey and calculate QQS for each service. The QQS is ranked on a scale of 1-10, with the higher value implying that subscribers are more satisfied with their service. The results of the study are shown below. Cable Sample Size Sample Mean Population Standard Deviation 50 8.8 3 50 Satellite 9.5 2 Is there persuasive evidence for the analyst to conclude at a = 0.05 that there is a difference in mean QQS between cable and satellite subscribers? If the calculated test statistic is |1.37|, what is the decision and conclusion for the hypothesis test? Select one: a. Fail to reject the Ho. There is sufficient evidence to conclude that the average QQS is significantly different between cable and satellite subscribers. b. Reject the Ho. There is not sufficient evidence to conclude that the average QQS is significantly different between cable and satellite subscribers. c. Reject the Ho. There is sufficient evidence to conclude that the average QQS is significantly different between cable and satellite subscribers. d. Fail to reject the H . There is not sufficient evidence to conclude that the average QQS is o significantly different between cable and satellite subscribers. Your answer is correct. n = 50, x = 8.8, σ = 3 (c refers to cable) c c c ns = 50, xs = 9.5, σs = 2 (s refers to satellite) Since we know both population standard deviations, we need to apply Z test statistics. With difference as the keyword in the claim, it is a two-tailed test, whichever mean value can go first in the numerator, thus final answer can either be positive or negative Ho : μc = μs H :μ ≠μ 1 c s Decision rule: reject H if Z > 1.96 or Z < -1.96 (0.5 - 2/a = 0.5 - 0.025 = 0.475 the area o corresponding to Z = 1.96) z = -1.37 or z = 1.37 Decision: Fail to reject the Ho. Conclusion: There is not sufficient evidence to conclude that the average QQS is significantly different between cable and satellite subscribers.  The correct answer is: Fail to reject the Ho. There is not sufficient evidence to conclude that the average QQS is significantly different between cable and satellite subscribers. Question 7 Correct Marked out of 1 You and some friends have decided to test the validity of an advertisement by Papa Jones Pizza, which says it delivers to UL dormitories faster than Domino's Pizza. You define the variable of interest as the delivery time, in minutes, from the time the pizza is ordered to when it is delivered. You collect the data by ordering 10 pizzas each from Papa Jones and Domino's at different times. Sample Mean Sample Standard Deviation Papa Jones 16.7 Domino's 3.0955 18.88 2.8662 At the 0.01 level of significance, is there evidence that the mean delivery time for Papa Jones Pizza is less than the mean delivery time for Domino's Pizza? Question to address here: what is the critical value for this problem? Select one: a. 2.567 b. 2.861 c. 2.552 d. 2.539 e. 2.845 Your answer is correct. Population standard deviation unknown, and no indication of whether the two population standard deviations equal or not, we automatically assume they are equal, or in other words, a pooledvariance test. DF = n1+n2-2=10+10-2=18, a = 0.01, "less than" indicating a one-tailed t test, thus critical value = 1.734 The correct answer is: 2.552  Question 8 Incorrect A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Marked out of 1 Sample Size Sample Mean Population Standard Deviation Men Women 25 30 23 28 5 10 At the .02 significance level, can we claim that there is a difference in the saving between women and men? What is the critical value for this hypothesis? Select one: a. 1.96 b. 2.399 c. 2.633 d. 2.05 e. 2.33 Your answer is incorrect. We know both population standard deviations, thus z test is needed. With the claim keyword "a difference", we are dealing with a two-tailed z test. Thus 0.5 - a/2 = 0.5 - 0.02/2 = 0.4900 the area. The closet area on z table to be found is 0.4901, which corresponds to z = 2.33. The correct answer is: 2.33  Question 9 Correct Marked out of 1 A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results related to the samples are presented below. Process A Process B Mean 0.002 mm 0.0026 mm Standard deviation 0.0001 mm 0.00012 mm Sample size 12 14 The researcher is interested in determining whether there is evidence that the two processes yield different average errors. Assume that the population standard deviations are equal. What is the Ho and H1 for the test? Select one: a. Ho: UA = UB H1: UA ≠ UB b. FHo: UA ≥ UB H1: UA < UB c. Ho: UA ≠ UB H1: UA = UB d. Ho: UA ≤ UB H1: UA > UB Keyword: "different average errors", we are dealing with a two-tailed test. Ho: UA = UB H1: UA ≠ UB The correct answer is: Ho: UA = UB H1: UA ≠ UB  Question 10 Incorrect Marked out of 1 A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income funds and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds? Question to address here: what's the p-value of the test? Select one: a. <0.01 b. <0.001 c. (0.001, 0.01) d. (0.0005, 0.005) e. >0.001 This is a t test when population standard deviations unknown but assumed equal, need to apply formula [11-6]. Income Funds Growth Funds Sample Size 35 Mean 900 40 875 Sample standard deviation 35 45 2 2 2 Pooled variance sp = [(35-1)*35 + (40-1)*45 ]/(34+40-2) = 1652.397 t = (900-875)/sqrt[1652.397(1/35 + 1/40)] = 2.657 df = 35+40 - 2 = 73 From the df line of 73, find the location of 2.657, which fits between 2.645 and 3.429; move up, find the two corresonding level of significance for two-tailed test since we are dealing with a twotailed test, 0.01 and 0.001. Thus the p-value for the test is (0.001, 0.01) The correct answer is: (0.001, 0.01) Return to: Module 2  