MGMT 650 Fall 2017 Problems Session 2 1) Using the data file, GRADSURVEY, answer the following: a) What does a row correspond to in the table? b) How many variables are measured on each row? c) For each variable, would you describe it as primarily categorical, or quantitative? If quantitative, what are the units? If categorical, is it ordinal or simply nominal? d) Are these data a time series, or are these crosssectional? 2. A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are under filled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truthin-labeling laws. In this example, the label weight on the package indicates that, on average, there are 5.5 grams of tea in a bag. If the average amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 170 bags a minute). The following table provides the weight in grams of a random sample of 50 bags produced in one hour by a single machine: 5.8 5.7 5.4 5.4 5.5 5.3 5.5 5.4 5.5 5.4 5 5.5 7 5.6 7 5.6 7 5.6 8 4 5.5 5.4 5.5 6 5.4 5 2 5.5 3 5.4 7 5.4 2 5.4 4 5.5 4 5.6 1 5.5 8 5.2 5 3 5.5 5 5.5 3 5.5 9 5.5 6 4 5.6 8 5.3 2 5.5 5.6 3 4 5.6 6 5 5.4 8 5.7 5.3 9 5.3 5.5 5.5 5.5 7 2 5.6 4 5.4 9 5.5 3 5.6 7 1 5.5 1 5.5 5 5.5 8 5.3 6 a. Compute the arithmetic mean and median. Do not compute by column. Consider all the data values given. b. Compute the first quartile and third quartile. c. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation. You are a consultant brought in by the company and given the sample results. What are your recommendations to the company, based on your reading for this week? d. Interpret the measures of central tendency within the context of this problem. Why should the company producing the tea bags be concerned about the central tendency? e. Interpret the measures of variation within the context of this problem. Why should the company producing the tea bags be concerned about variation? 3. According to Zillow.com, here is a list of the prices of the property sold (in thousands) in Washington, DC June 29 - 30, 2016. 31 146 133 177 580 192 440 844 443 785 6 0 3 5 26 5 29 9 86 9 24 0 131 721 368 763 5 145 105 320 918 1 170 245 146 920 0 0 0 125 142 145 585 0 0 6 187 121 5 3 157 187 625 673 449 0 9 156 175 780 888 495 2 0 143 147 949 945 645 5 5 536 406 961 a) Use the house price data and five bins to create a histogram using the data analysis tool. b) Create another histogram with 10 bins. Compare the two. Which is better and why? 4. As part of the marketing group of a film company, you are asked to find out the age distribution of the audience of the latest film. You ask questions of customers who exit the theatre. From 470 responses, you find that 45 are younger than 6 years old, 83 are 6 to 9 years, 154 are 10 to 14, 18 are 15 to 21, and 170 are older than 21. a) Make a frequency table of these categorical data. b) Make a relative frequency table. c) Make a bar chart using counts in the frequency table. d) Would a bar chart of relative frequencies look any different? e) Make a pie chart. f) Write a few sentences summarizing the distribution demonstrated by your charts and tables. 5. In addition to age grouping information, the audiences interviewed were also asked if they had seen the movie before (Never, Once, More than Once). The two-way contingency table shows the results. never once more than once unde r6 39 3 6 to 9 60 20 3 3 10 to 15 to over 14 21 21 84 16 151 38 2 15 32 0 4 a) Find the marginal distributions of their previous viewing of the movie. b) Verify that the marginal distribution of the ages is the same as that given previously. c) Find column percentages. d) Looking at these percentages, does the distribution of how many times someone has seen the movie look the same for each age group? e) Make a stacked bar chart showing the distribution of viewings for each age level 6) Age 20 30 38 25 35 32 30 22 22 42 34 14 44 32 44 A survey of customer age also asked about gender. Gend er m f f m f f m m m f f m f f f 29 29 48 35 44 30 11 26 32 48 m m f f f m m f f f Compare critical descriptive statistics for males and females. Write a sentence or two summarizing what you found