1. The data set below contains spending on products ($) during a three-month period by a sample of 15 customers receiving incentives through a mobile loyalty program. Complete parts (a) through (d) below. 55.79 22.77 67.79 46.61 57.31 108.75 50.39 35.52 78.78 50.89 63.44 59.64 41.25 56.76 53.54 a. Compute the mean and median. The mean is nothing . (Round to two decimal places as needed. Do not include the $ symbol in your answer.) The median is nothing . (Round to two decimal places as needed. Do not include the $ symbol in your answer.) b. Compute the variance, standard deviation, range, and coefficient of variation. The variance is nothing . (Round to two decimal places as needed. Do not include the $ symbol in your answer.) The standard deviation is nothing . (Round to two decimal places as needed. Do not include the $ symbol in your answer.) The range is nothing . (Round to two decimal places as needed. Do not include the $ symbol in your answer.) The coefficient of variation is nothing %. (Round to two decimal places as needed.) c. Are the data skewed? If so, how? A. No comma the data are not skewed.No, the data are not skewed. B. Yes comma the data are left dash skewed.Yes, the data are left-skewed. C. Yes comma the data are right dash skewed.Yes, the data are right-skewed. D. There is not enough information to determine the skewness of the distribution. d. Based on the results of (a) through (c), what conclusions can be reached concerning spending on products by customers receiving incentives through a mobile loyalty program? The average amount spent is $ nothing and half the customers spent more than $ nothing . The average scatter of the amount around the mean is $ nothing . The difference between the highest amount spent and lowest amount spent is $ nothing . (Round to the nearest cent as needed.) 2. Form an ordered array, given the following stem-and-leaf display from a sample of n equals 7n=7 midterm exam scores in information systems. 59 6 7 459 8 57 93 The ordered array is nothing . (Use a comma to separate answers as needed.) 3. An institute surveyed small business owners across a state that employed 50 or fewer employees. The purpose of the study was to gain insight on the current small business health-care environment. Small business owners were asked if they offered health-care plans to their employees and if so, what portion (%) of the employee monthly health-care premium the business paid. The accompanying frequency distribution was formed to summarize the portion of premium paid for 8383 small businesses who offer health-care plans to employees. Complete parts (a) through (c). Portion of Premium Paid (%) Frequency less than 1% 2 1% but less than 26% 7 26% but less than 51% 18 51% but less than 76% 20 76% but less than 100% 22 100% 14 a. What percentage of small businesses pays less than 26% of the employee monthly health-care premium? nothing % (Round to two decimal places as needed.) b. What percentage of small businesses pays between 26% and 75% of the employee monthly healthcare premium? nothing % (Round to two decimal places as needed.) c. What percentage of small businesses pays more than 75% of the employee monthly health-care premium? nothing % (Round to two decimal places as needed.) 4. A categorical variable has three categories, with the frequencies of occurrence below. a. Compute the percentage of values in each category. b. What conclusions can you reach concerning the categories? CategoryFrequency A 16 B 27 C 7 a. Complete the table below. CategoryFrequency A 16 B 27 C 7 Percentage (%) nothing % nothing % nothing % (Simplify your answers.) a. Complete the table below. CategoryFrequency A 1616 B 2727 C 77 Percentage (%) nothing % nothing % nothing % (Simplify your answers.) b. What conclusions can you reach concerning the categories? A. Category B occurs more than half of the time. The other two categories occur less than half of the time, with category A being the least likely to occur. B. Category B is the most likely to occur while category C is the least likely to occur. All three categories occur more than a quarter of the time. C. Category B occurs more than half of the time. The other two categories occur less than half of the time, with category C being the least likely to occur. D. Category B is the most likely to occur while category C is the least likely to occur. All three categories occur less than half of the time. E. Category C occurs more than half of the time. The other two categories occur less than half of the time, with category B being the least likely to occur. 5. The following is a set of data from a sample of n equals 5n=5. 5 8 3 9 10 a. Compute the mean, median, and mode. b. Compute the range, variance, standard deviation, and coefficient of variation. c. Compute the Z scores. Are there any outliers? d. Describe the shape of the data set. a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is nothing . (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed) B. There is no solution. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The median is nothing . (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed) B. There is no solution. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode is nothing . (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed) B. There is no solution. b. The range is nothing . (Type an integer or a decimal. Do not round.) The variance is nothing . (Type an integer or decimal rounded to two decimal places as needed.) The standard deviation is nothing . (Type an integer or decimal rounded to two decimal places as needed.) The coefficient of variation is nothing %. (Type an integer or decimal rounded to two decimal places as needed.) c. Compute the Z scores. Data (X) 5 Z Score nothing (Round to two decimal places as needed.) nothing 8 3 9 10 nothing nothing (Round to two decimal places as needed.) (Round to two decimal places as needed.) (Round to two decimal places as needed.) nothing (Round to two decimal places as needed.) Are there any outliers? Yes No d. What is the shape of the data set? Negative left parenthesis left dash skewed right parenthesisNegative (left-skewed) Positive left parenthesis right dash skewed right parenthesisPositive (right-skewed) SymmetricalSymmetrical 6. Suppose that 10,000 customers in a retailer's customer database are categorized by three customer types: 3,500 prospective buyers, 4,500 first time buyers, and 2,000 repeat (loyal) buyers. A sample of 1,000 customers is needed. Complete parts (a) through (c) below. a. What type of sampling should you do? Why? A. Simple random sample for accuracy B. Stratified sample for efficiency C. Convenience sample for efficiency D. Systematic sample for accuracy b. Explain how you would carry out the sampling according to the method stated in (a). A. Select a simple random sample from each of the three types of customers and combine the results. B. Take a simple random sample of 500 of the customers out of all of the customers, disregarding which stratum each customer belongs to. C. Partition the N customers in the frame into n groups of k customers, where kequals=StartFraction Upper N Over n EndFractionNn, rounding to the nearest integer. Next, choose the first customer to be selected at random from the first k customers in the frame. Then, select the remaining nminus1 customers by taking every kth customer thereafter from the entire frame. D. Take the highest number of samples from the stratum that seems the most representative, and take the lowest number of samples from the stratum that is most likely to produce outliers. c. Why is the sampling in (a) not simple random sampling? A. A simple random sample gives every item from a frame the same chance of selection as every other item, which is not true with this sampling method. B. The probability of selection for each customer must be known, which is not true with this sampling method. C. A simple random sample gives every sample of a fixed size the same chance of selection as every other sample of that size, which is not true with this sampling method. D. In a simple random sample, each customer must be replaced in the sample after being chosen, which is not true with this sampling method. 7. The following information is collected from students upon exiting the campus bookstore during the first week of classes. a. Number of siblingsNumber of siblings b. Method of paymentMethod of payment c. WeightWeight d. Dorm hall of residenceDorm hall of residence Classify each of these variables as categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. a. Number of siblingsNumber of siblings is what type of variable? Numerical comma continuousNumerical, continuous CategoricalCategorical Numerical comma discreteNumerical, discrete b. Method of paymentMethod of payment is what type of variable? Numerical comma discreteNumerical, discrete CategoricalCategorical Numerical comma continuousNumerical, continuous c. WeightWeight is what type of variable? Numerical comma continuousNumerical, continuous Numerical comma discreteNumerical, discrete CategoricalCategorical d. Dorm hall of residenceDorm hall of residence is what type of variable? Numerical comma discreteNumerical, discrete Numerical, continuous CategoricalCategorical 8. For the companies in which they invest, pension fund managers seek to ensure the independence of the boards of directors. For one company, fund managers determine that the board had 6 inside directors, 3 independent (outside) directors, and 6 directors that the company labeled as independent, but whom officials consider to be insiders. Seeking more independence of this board, the fund managers ask for change. The company responds and fund managers evaluate the company's new board as having 3 inside directors, 9 independent directors, and 5 directors improperly labeled as independent. Examine the two accompanying charts that are based on these findings and complete the questions below. Chart1. Chart2. If you were a corporate affairs officer at the company, would you choose Chart1 or Chart2 to highlight the changes in the composition of the board? Explain your answer. A. Chart2long dashthis chart provides the relative frequency of the three types of directors before and after the reform. Chart2 provides more information. B. Chart1long dashthis chart provides the relative frequency of the three types of directors before and after the reform. Chart1 provides more information. C. Chart1long dashthis chart provides both the frequency and relative frequency of the three types of directors before and after the reform. Chart1 provides more information. D. Chart2long dashthis chart provides both the frequency and relative frequency of the three types of directors before and after the reform. Chart2 provides more information. If you were one of the pension fund managers seeking to ensure an independent board of directors, which chart would you choose? Explain your answer. A. Chart2long dashthis chart shows the relative frequency of independent directors, showing that the board is composed mostly of independent directors after the reform through percentages. B. Chart1long dashthis chart shows the relative frequency of independent directors, showing that the board is composed mostly of independent directors after the reform through percentages. C. Chart1long dashthis chart shows the frequency of independent directors, showing that the board is composed mostly of independent directors after the reform through percentages. D. Chart2long dashthis chart shows the frequency of independent directors, showing that the board is composed mostly of independent directors after the reform through percentages