University of Puerto Rico Mayagez Ca mpus College of Business Administration ESTA 3002 Business Statistics Dra. Rosario de los A. Ortiz Rodrguez Spring 2015 Name__________________________ Date ______________________ Section ______ Exam III Please read carefully. You must show all of your work for full credit. A correct answer with no work shown is worth no points, but an incorrect or partial answer with some work shown may be worth partial credit. Please follow the instructions given in class. For Problems I to VI state just the null and alternative hypotheses and chose from the list below the appropriate statistical method a. Hypothesis testing about the difference in two means using the z statistic (population variances known), b. Confidence intervals about the difference in two means using the z statistic (population variances known), c. Hypothesis testing about the difference in two means: independent samples and population variances unknown but equal d. Confidence intervals about the difference in two means: independent samples and population variances unknown but equal e. Hypothesis testing about the difference in two means: independent samples and population variances unknown but different f. Confidence intervals about the difference in two means: independent samples and population variances unknown but different g. Statistical inferences for two related populations h. Hypothesis testing about two population proportions i. Confidence intervals about two population proportions j. Testing hypotheses about two population variances k. The completely randomized design (one-way ANOVA) l. Multiple comparison tests Page 1 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM I. When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie- laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. (Data extracted from \"Drilling Down, Sizing up a Cheeseburger's Caloric Heft,\" The New York Times, October 4, 2010, p. B2.) Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first. a) State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first. b) Determine the appropriate statistical method for this problem? c) What assumption is necessary about the population distribution in order to perform the test in Page 2 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM II. A recent study (\" Snack Ads Spur Children to Eat More,\" The New York Times, July 20, 2009, p. B3) found that children who watched a cartoon with food advertising ate, on average, 28.5 grams of Goldfish crackers as com-pared to an average of 19.7 grams of Goldfish crackers for children who watched a cartoon without food advertising. Although there were 118 children in the study, neither the sample size in each group nor the sample standard deviations were reported. Suppose that there were 59 children in each group, and the sample standard deviation for those children who watched the food ad was 8.6 grams and the sample standard deviation for those children who did not watch the food ad was 7.9 grams. Assuming that the population variances are equal and = 0.05 a) State the null and alternative hypotheses if you want to determine whether the mean amount of Goldfish crackers eaten was significantly higher for the children who watched food ads? b) Determine the appropriate statistical method for this problem? Page 3 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM III. Multiple myeloma, or blood plasma cancer, is characterized by increased blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient's own stem cells. The data stored in Myeloma, and shown below, represent the bone marrow micro vessel density for patients who had a complete response to the stem cell transplant (as measured by blood and urine tests). The measurements were taken immediately prior to the stem cell transplant and at the time the complete response was determined. PATIENT 1 2 3 4 5 6 7 BEFORE 158 189 202 353 416 426 441 AFTER 284 214 101 227 290 176 290 Data extracted from S. V. Rajkumar, R. Fonseca, T. E. Witzig, M. A. Gertz, and P. R. Greipp, \" Bone Marrow Angiogenesis in Patients Achieving Complete Response After Stem Cell Transplantation for Multiple Myeloma,\" Leukemia 13 ( 1999): 469- 472. a) State the null and alternative hypotheses if you want to determine whether the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell trans-plant? b) Determine the appropriate statistical method for this problem? c) What assumption is necessary about the population distribution in order to perform the test in? Page 4 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM IV. Will improving customer service result in higher stock prices for the companies providing the better service? \"When a company's satisfaction score has improved over the prior year's results and is above the national average (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run\" (Businessweek, March 2, 2009). The following satisfaction scores of three companies for the 4th quarters of 2007 and 2008 were obtained from the American Customer Satisfaction Index. COMPANY RITE AID EXPEDIA J.C. PENNEY 2007 SCORE 73 75 77 2008 SCORE 76 77 78 Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the population standard deviation can be assumed to equal 6 points in each case. a) State the null and alternative hypotheses if you want to determine whether for Rite Aid the increase from 2007 to 2008 is statistically significant. b) Determine the appropriate statistical method for this problem? Page 5 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM V. Do social recommendations increase ad effectiveness? A study of online video viewers compared viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. Data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. The results were: CORRECTLY RECALLED THE BRAND ARRIVAL METHOD RECOMMENDATION BROWSING YES 407 93 NO 150 91 Source: Data extracted from \"Social Ad Effectiveness: An Unruly White Paper,\" www.unrulymedia.com, January 2012, p. 3. a) State the null and alternative hypotheses if you want to determine whether brand recall is higher following a social media recommendation than with only web browsing b) Determine the appropriate statistical method for this problem? Page 6 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM VI. QSR has been reporting on the largest quick- serve and fast- casual brands in the United States for nearly 15 years. The QSR contains the food segment (burger, chicken, pizza, or sandwich) and U. S. average sales per unit ($ thousands) for each of 58 quick- service brands. ( a) State the null and alternative hypotheses if you want to determine whether there is difference in the mean US average sales per unit ($ thousands) among the food segments? b) Determine the appropriate statistical method for this problem? Page 7 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM VII. A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting times (measured from check- in to when the patient was called into the clinic area) were collected and stored as follow SUMMARY Groups Main Satellite 1 Satellite 2 Satellite 3 ANOVA Source of Variation Between Groups Within Groups Total Count 15 15 15 15 SS A B 24805.54 Sum Average Variance 1047.64 69.84267 331.3198 618.81 41.254 375.976 848.42 56.56133 205.3533 779.58 51.972 408.2862 df C D MS 2104.15 F F G E Page 8 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM a) Complete the above table A. B. C. D. E. F. G. b) For this problem at the 0.05 level of significance we reject the null hypothesis, there is statistically evidence that at least one of the mean waiting times in the four locations is different. Determine which locations differ in mean waiting time, at =0.05. Page 9 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM VIII. An important feature of digital cameras is battery life, the number of shots that can be taken before the battery needs to be recharged. The file Cameras contains the battery life of 11 subcompact cameras and 7 compact cameras. (Data extracted from \"Cameras,\" Consumer Reports, July 2012, pp. 42- 44.) Subcompact Mean Standard Error Median Standard Deviation Sample Variance Minimum Maximum Sum Count Compact 207.27 8.95 210 29.70 220.00 21.93 230 58.02 881.82 150 250 2280 11 3366.67 130 310 1540 7 a. Is there evidence of a difference in the variability of the battery life between the two types of digital cameras? (Use = 0.05.) b. What assumption about the population distribution of the two types of cameras is necessary? Page 10 of 10 ESTA 3002 EX 3 Spring 2015 Dra. Rosario de los A. Ortiz Rodrguez UPRM