Problem 3.38: Nielsen Monitor-Plus a service of Nielsen Media Research is one of the leaders in advertising information services in the United States providing advertising activity for 16 media including television tracking in all 210 Designated Market Area (DMAs). One of the issues it has research is the increasing amount of “clutter”-nonprograming minutes in an hour of prime time including network and local commercials and advertisements for other shows. Recently it found the average nonprogramming minutes in an hour of prime-time broadcasting for network television was 15:48 minutes. For cable television the average was 14:55 minutes. a. Calculate the difference in the average clutter between network and cable television. b. Suppose the standard deviation in the amount of clutter for both the network and cable television was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two clutter averages? Comment. Problem 3.49: Consider the following set of sample data: 78 121 143 88 110 107 62 122 130 95 78 139 89 125 a. Compute the mean and standard deviation for these sample data. b. Calculate the coefficient of variation for these sample data and interpret its meaning c. Using Tchebysheff’s Theorem determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not. Problem 3.56: Consider the following population: 71 89 65 97 46 52 99 41 62 88 73 50 91 71 52 86 92 60 70 91 73 98 56 80 70 63 55 61 40 95 a. Determine the mean and variance. b. Determine the percentage of data values that fall in each of the following intervals: .0/msohtmlclip1/01/clip_image002.gif”> c. Compare these with the percentages specified by Tchebysheff theorem. Problem 3.61 Anaheim Human Resources Inc. performs employment screenings for large companies in southern California. It usually follows a two-step process. First potential applicants are given a test that covers basic knowledge and intelligence. If applicants score between a certain range they are called in for a interview. If they score below a certain point they are sent a rejection letter. If applicants score above a certain point they are sent directly to client’s human resources office without the interview. Recently Anaheim Human Resources began working with a new client and formulated a new test just for this company. Thirty people were given the test which is supposed to produce scores that are distributed according to a bell-shaped distribution. The following data reflect the scores of those 30 people: 76 75 74 56 61 76 62 96 68 62 78 76 84 67 60 96 77 59 67 81 66 71 69 65 58 77 82 75 76 67 Anaheim Human Resources has in the past issued a rejection letter with no interview to the lower 16% taking the test. They also send the upper 2.5% directly to the company without an interview. Based on the data the assumption of a bell-shaped distribution what score should be used for the two cutoffs? Problem 3.38: First you will need to convert the means to measures in minutes. No further hints.Problem 3.49: Tools required for part a are already familiar to you by now. Part b’s reference to the coefficient of variation can be found on p.119 and Tchebysheff’s Theorem (used for non-normal data) is explained on p. 121.Problem 3.56: Hints for this problem have already been covered in Problem’s 3.49 hints.Problem 3.61: You will need to compute the mean and standard deviation of this data and then use what you know about the Empirical Rule (pp. 120-121) to answer this question. Pay attention to Figure 3.8 on p. 120. Notice for example that two standard deviations on either side of the mean contains (in theory) 95% of the data. That means that 2.5% of the data is to the left of that zone (on the low end of the distribution) and 2.5% of the data is to the right of that zone (on the high end of the distribution). So if you wanted to calculate the cutoff that gives you the upper 2.5% of the distribution for example you would need to take the mean of your dataset and add to that two standard deviations.
