Instructions: The solutions you submit must be your own work. All written, text-based responses must be in your own words. You are welcome to consult with classmates on the computing aspects, but if you do, please provide their names in your solutions document. See accompanying file: MM_BABS550_2016_Asst2_DATA.xlsx for data sets (in Excel). Question 2 - Recognition in the Workplace What are the most preferred forms of recognition in the workplace? In a survey by Office Arrow, 163 of 388 administrative professionals responded that verbal recognition is the most preferred form of recognition, and 74 responded that cash bonuses are most preferred. (Source: \"Most Preferred Forms of Recognition at Workplace,\" USA Today, May 2009) a) Compute the standard error of the sample proportion and construct a 95% confidence interval estimate for the population proportion of administrative professionals who prefer verbal recognition. b) Compute the standard error of the sample proportion and construct a 95% confidence interval estimate for the population proportion of administrative professionals who prefer cash bonuses. c) Write a one sentence explanation for each of the two intervals you computed in parts a) and b). Make sure they are both statistically accurate and grammatically correct! d) What sample sizes would be needed for each 95% confidence interval to have a margin of error to be 3%? Remember to use the results from the survey, not the short-cut formula. Which value would you recommend to the survey researchers? 1 Question 3 - Response Time for Customer Complaints One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large department store selling furniture, flooring, and carpeting underwent a major expansion. The store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 50 complaints made in the last year. The data are given in the worksheet Furniture, and are also presented here. 54 74 94 29 4 5 27 31 26 52 35 11 26 25 30 137 19 5 1 22 31 126 12 14 36 27 110 4 13 26 152 110 165 13 20 2 29 32 10 23 123 61 29 5 33 81 35 28 27 68 a) Draw a histogram to decide whether the distribution is approximately normal. b) What is the shape of the sampling distribution of the mean response time? Justify your choice of type of distribution. c) Construct a 95% confidence interval for the population mean number of days between receiving a complaint and the resolution of the complaint. d) Will the interval contain the response times of approximately 95% of similar complaints? Explain your answer in one or two sentences. e) The installation supervisor claims that the mean number of days between receiving a complaint and the resolution of a complaint is 25 days. At the 5% significance level, is there evidence that the claim is not true (i.e. that the mean number of days is different from 25)? (i) Formulate this problem as a hypothesis test. Give the null and alternative hypotheses. Should you use a one-sided or a two-sided alternative? Explain. (ii) Carry out the hypothesis test. Report the test statistic and the P-value. State your conclusion clearly and concisely in the context of the question. (iii) Does the 95% confidence interval from part (c) support the conclusion of your hypothesis test? Explain. f) Describe in words what is meant by Type I error and a Type II error in this situation. Based on your analysis in part (e), only one of those errors could have happened; which one? g) The installation supervisor thinks that the 5 largest response times shouldn't be included because there were unusual circumstances with those complaints. Redo the hypothesis test with the 5 largest response times excluded. Does the conclusion change? 2 Question 4 - Real Estate The sales price of a home certainly depends on its size and features (e.g. fireplaces). From a larger data set of over one thousand homes, two random samples of 50 listings each have been extracted. One sample has houses with fireplaces and the other has houses without fireplaces. The worksheet RealEstate also has: Price ($), Living Area (sq ft), and Age (years) for each listing. a) Carry out three hypothesis tests to see whether there is a real difference in mean price, mean living area, and mean age of these two populations (i.e. with and without fireplaces). Note: You may use Excel or, if you prefer, you may do the calculations manually. You do not need to report the details; for each test just report the hypotheses, test statistic value, P-value and a well-articulated conclusion. The level of significance is not specified, so draw your conclusions by referring to the strength of evidence indicated by the P-value. b) For the difference in mean house prices, find a 95% confidence interval. [You don't need to compute CIs for the other two variables.] Explain in one sentence how the first hypothesis test in part a) (comparing mean price) and this confidence interval reflect the relationship between confidence intervals and hypothesis tests. Question 5 - Taste Tests and Tasty t-tests You are a marketing manager at PepsiCo and have gathered taste test data. Your biggest competitor for one of your leading soft drinks (Diet Pepsi) is Diet Coke. In your study you invited a random sample of individuals to participate in a focus group. Each participant was presented with the colas in random order with a glass of water to sip in between. Participants rated each cola on a scale from 1 to 7 (higher is better). See the TasteTest worksheet on the accompanying data spreadsheet. Column H indicates which cola each subject tasted first. IMPORTANT: In the accompanying spreadsheet, Cola A = Pepsi, Cola B = Coca Cola. Hint: Currently Pepsi and Coca Cola data are mixed together in a single column. You will need to rearrange the data by cutting and pasting so that, for each of the three areas (taste, freshness, and quality) all the Pepsi data are in one column and all the Coca Cola data in another column. a) Carry out three hypothesis tests from the perspective of PepsiCo to see whether their product is the preferred cola in the separate areas of taste, freshness, and quality. Use a 0.05 level of significance. b) Now construct three 95% confidence intervals to supplement the three hypothesis tests you carried out in part a). Do the confidence intervals confirm the conclusions in part a)? c) Explain very briefly what would change in your computations and results if you carried out the hypothesis tests and confidence intervals from the perspective of Coca Cola. 3 Question 6 - Coffee Consumption in Canada (Mini Case Study Project, p. 434) Please read the description on p. 434 for details of the case. A survey of a national sample of 2101 adults asked a question about coffee consumption that grouped people into three types of drinkers: serial drinker, borderline problem, or casual consumer. Then \"type of drinker\" was crosstabulated by region, gender and age. Here are the three crosstabs. Type of Drinker Serial Drinker Borderline Problem Casual Consumer Total West 74 258 298 630 Type of Drinker Serial Drinker Borderline Problem Casual Consumer Total Male 99 370 545 1014 Type of Drinker Serial Drinker Borderline Problem Casual Consumer Total 18-34 94 211 264 569 Region Ontario Quebec 113 45 346 204 361 255 820 504 Gender Female 152 503 432 1087 Age Groups 35-54 113 375 345 833 Atlantic 19 65 63 147 Total 251 873 977 2101 Total 251 873 977 2101 55+ 44 287 368 699 Total 251 873 977 2101 Use hypothesis tests to examine the relationships between type of drinker and these three demographic variables. Remember to state the hypotheses, test statistics (detailed calculations are not necessary to show), P-values, and conclusions. *** END *** 4 ResponseTime 54 5 35 137 31 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 165 32 29 28 29 26 25 1 14 13 13 10 5 27 4 52 30 22 36 26 20 23 33 68 Price ($) Living Area (sq ft) 168,065 1,016 51,183 1,144 107,912 1,308 80,540 1,380 93,895 960 62,105 1,228 80,248 1,600 208,635 2,714 105,843 972 155,787 1,540 141,760 1,740 125,029 1,836 135,823 1,946 139,219 2,308 99,045 937 89,232 960 91,672 1,392 134,378 1,279 79,982 1,572 72,189 1,594 175,784 1,837 154,723 1,944 130,518 1,200 135,708 1,460 107,743 1,228 104,339 1,290 117,907 1,295 114,070 1,098 108,459 1,292 94,667 912 31,113 1,540 91,792 908 140,765 1,596 114,513 1,560 91,672 929 65,550 1,196 114,514 1,514 138,914 1,576 111,875 1,758 123,827 1,302 104,084 1,170 122,221 1,170 183,066 1,836 90,446 1,256 77,547 908 109,249 812 94,868 1,380 109,577 1,456 69,876 976 Age (years) 41 15 26 0 48 53 16 1 40 16 36 27 18 5 19 51 21 31 41 81 18 0 1 17 21 16 125 113 25 34 115 17 49 5 21 56 17 18 25 35 10 26 9 19 19 115 105 155 21 Fireplace 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 98,389 140,269 217,226 154,696 189,108 164,623 200,126 153,129 144,571 262,461 224,818 262,461 271,578 334,556 188,497 154,432 149,756 223,266 178,851 173,446 237,583 294,133 162,091 186,348 190,444 113,367 236,742 143,210 163,652 198,083 212,846 159,843 158,338 176,698 159,786 119,389 345,364 130,490 295,268 226,304 119,858 181,225 181,140 109,259 139,800 167,693 312,434 126,049 106,365 101,418 1,184 1,244 2,593 1,704 2,097 1,772 1,690 1,872 1,512 2,505 2,738 2,932 3,123 3,376 2,110 1,644 1,470 2,619 2,002 2,124 2,762 3,981 1,806 2,011 1,836 1,760 2,412 1,744 1,908 1,971 2,270 1,350 1,836 1,772 1,561 1,364 3,308 1,595 4,534 1,921 1,476 1,944 2,310 1,239 1,900 1,876 3,440 1,268 1,184 1,852 18 13 0 17 10 0 5 32 13 1 12 31 14 7 9 20 11 4 14 0 17 0 0 14 0 133 10 35 25 7 0 1 15 14 16 20 7 6 15 0 24 25 31 33 12 1 3 25 20 37 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 223,055 2,668 0 1 Ratings of Cola Tasted First Ratings of Cola Tasted Second First Pre Taste Pre Fresh Pre Quality Post Taste Post Fresh Post Quality Cola (A=Pepsi) ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 5 7 6 6 6 6 7 2 7 7 7 6 6 6 6 4 1 5 1 2 5 2 2 6 6 4 3 5 1 5 5 0 2 5 5 2 6 7 7 2 3 4 4 4 6 4 7 2 5 7 7 6 4 7 4 4 1 3 4 4 4 4 2 4 3 4 3 6 2 3 4 0 5 4 5 4 4 7 4 7 4 7 5 4 6 5 7 2 6 7 7 5 4 6 6 4 1 4 3 4 4 3 2 4 5 4 4 6 1 3 5 0 4 5 5 3 5 7 4 2 5 3 6 5 6 6 7 2 7 7 6 2 4 5 7 6 1 7 7 2 3 2 2 1 2 2 6 2 6 3 3 4 4 2 5 2 3 5 2 3 3 4 5 4 6 4 4 2 5 7 6 3 4 6 7 4 1 4 7 2 3 3 3 1 4 2 2 1 4 5 4 4 4 3 4 4 3 5 4 0 3 3 6 4 6 6 5 2 6 7 6 2 4 5 7 5 1 7 7 2 3 2 2 2 3 2 5 2 6 5 3 4 4 2 5 3 3 5 4 3 B A B A B B B A A A A A B A B A B B B B B B A A A B B B B B A B B B A A A B A A