An expert who works for a car magazine obtained random data (rounded to the near

Question

An expert who works for a car magazine obtained random data (rounded to the nearest thousand) among two categories of used or new cars:

Domestic
Foreign

The expert would like to understand sales based on list price (rounded to the nearest thousand dollars), sale price (rounded to the nearest thousand dollars), and number of days it takes to sell each car. The complete data set is in the file named Cars.

Managerial Report

Prepare a report (see below) that summarizes your assessment of the nature of the car market. Be sure to include the following seven items in your report.

1 Descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Domestic cars. Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier. If a result is an outlier, state whether it is below or above the mean.

2 Descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Foreign cars. Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier. If a result is an outlier, state whether it is below or above the mean.

3 Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the car expert understand the car market.

4 Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Domestic cars. What is the Margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

5 Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Foreign cars. What is the Margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

6 Assume the car expert requested estimates of the mean number of days to sell for the Domestic cars with a margin of error of seven days and the mean number of days of Foreign cars with a margin of error of eight days. Using 98% confidence, how large should the sample sizes be for each?

7 Suppose a Domestic car has a list price of $30,000 and a Foreign car has a list price of $30,000. What is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these cars?

Domestic Cars Foreign Cars Car List Price in K Sale Price in K Days to Sell List Price in K Sale Price in K Days to Sell 1 6.1 4.4 36 83.1 78.5 101 2 67.6 66.8 51 59.6 57.1 62 3 14 13.4 87 37 32.5 63 4 83.4 80.5 80 43.4 43.2 47 5 40 35.4 38 16.3 15 93 6 56 52 24 8.3 5.9 21 7 71.2 68.7 27 29.2 27.5 107 8 50.7 49.7 52 32.7 32.7 15 9 4.9 4.3 74 23.9 23.5 12 10 70.5 66.5 84 85.5 85.1 58 11 58 56 30 19 16.3 96 12 75 73.7 31 19 18.9 106 13 2.8 1.1 88 80.8 77.4 50 14 7.7 4 11 17.7 15.6 42 15 20 16.2 20 71.4 70.4 75 16 23 21.5 71 16.1 13.8 62 17 6.2 6 88 49.2 45.2 91 18 18 14 43 40 38 6 19 97 93.2 95 32 29.2 52 20 69.2 66.8 37 27.2 22.5 71 21 63.5 60.7 13 85.5 82.8 106 22 65 61.9 60 87.4 85.7 91 23 9.9 7 24 58.9 56.9 83 24 90.2 88.3 42 56.2 52.8 29 25 56 55 91 13.5 10 76 26 80 75.2 39 55.7 54.2 40 27 58.7 58.3 58 75.7 74.6 47 28 33.1 32.9 47 89.1 85.7 67 29 31.5 28.7 86 3.5 3.2 106 30 54.5 54.1 88 67.5 65.3 100 31 22.4 17.8 30 41.4 40.1 10 32 40.3 38.4 29 45.3 43.3 36 33 27.2 22.6 34 87.2 85.1 61 34 14.4 14.1 12 16.4 14.3 65 35 5.6 1.5 86 32.6 29.1 25 36 42.2 40.8 72 14.2 14.2 39 37 9.5 6.2 69 60.5 59.1 79 38 93.1 90.5 32 73.1 68.3 83 39 10.7 7.3 15 48.7 44.7 65 40 93.3 91.7 15 38.3 38.2 35 41 50 49.1 19 6.6 4.3 6 42 33.2 29.6 27 86.2 81.4 53 43 67 60 18 5 4.6 108 44 56 53.1 54 37 32.7 85 45 49.5 48.2 37 23.5 21.2 32 46 52.7 48.8 66 90.7 87.4 97 47 41.1 39.7 78 84.1 83.8 16 48 72.1 70.9 12 45.1 42.7 38 49 50 46.9 84 51.7 49.9 53 50 88 84.2 20 36 34.6 97 51 11.8 11.3 20 66.8 65 45 52 69.5 69 90 54.5 50.2 31 53 63 62.6 35 33 33 44 54 60 58.1 46 11.4 10.8 92 55 66.7 66.1 47 59.7 57.9 49 56 58 55.5 51 84.2 80.1 52 57 67.2 62.7 96 48.2 43.4 101 58 74.9 70.4 59 68.9 64.9 14 59 71.4 70.2 14 60.4 59.9 98 60 71.1 67.8 75 87.1 85.1 90 61 54 54 52 68.3 66.4 61 62 19.9 17.2 60 8.9 7.5 32 63 49.5 48.6 56 39.5 39.3 48 64 56.8 54.8 11 57.8 53.1 29 65 74 71.3 71 59 57.5 98 66 20.4 17 31 22.4 19.4 6 67 34.5 32.5 40 78.5 77.3 6 68 17.2 14.4 29 11.2 9.4 83 69 45 42.5 72 86.2 82 79 70 82 81 32 4 3.5 70 71 40 39.3 21 22.6 21.1 38 72 16 12.4 62 36 36 18 73 25 20.1 72 88 87.1 26 74 64.1 61.5 10 88.1 85.2 41 75 39.5 35.4 71 66.5 61.8 100 76 72 67.3 97 4.1 3.1 7 77 13 10.4 80 22 20.6 11 78 37.1 36.1 26 71.1 70.5 33 79 67.7 62.7 29 36.7 33.5 42 80 40 36.6 28 69.2 66.3 9 81 55.9 52.8 71 14.9 12.6 94 82 51 47.4 81 81 78.8 104 83 50 45.4 41 46.9 44.3 25 84 44.2 41 15 11.2 6.6 69 85 12 9.8 31 7 5.3 66 86 72 70 78 36 31.9 52 87 51.6 46.6 84 49.6 46.8 39 88 54.4 52.6 26 42.4 38.3 92 89 44.5 42.5 92 4.5 4 46 90 61.6 60.9 19 31.6 31 64 91 34.1 33.1 91 57.1 53.3 38 92 80 79 38 42 39 64 93 61.9 61.1 85 71.9 71 11 94 74.6 73.4 84 86.6 86.5 11 95 17 14.5 90 90 87.2 6 96 10.8 7.9 70 47.8 42.9 73 97 44.7 43.8 61 52.7 52.6 66 98 11.7 10.3 73 35.7 32 31 99 97.9 95.9 92 44.9 43.3 24 100 67.5 63 10 21.5 19.4 89 101 64 61.9 43 84.3 83.2 31 102 97.7 93.7 73 69.7 65.7 100 103 8.9 6.5 87 37.9 37.9 43 104 51.3 47.7 18 49.3 45.5 18 105 56 53.1 47 82.7 82.5 67 106 12.6 8.4 95 3.6 3.2 7 107 42.6 38.7 73 53.6 48.9 87 108 50 47.7 84 74.2 69.2 11 109 25.7 24.8 38 56.7 53.2 50 110 72.4 67.6 98 54.4 51 69 111 20.7 18.3 16 38.7 34 28 112 62.3 57.9 13 4.3 2.9 85 113 41.4 37.4 61 19.4 15.9 7 114 50 49 97 16.5 12.8 95 115 77.9 76.7 84 41.9 41 52 116 10 9.2 25 73 69.4 98 117 80 76.1 44 56 55.9 68 118 61.5 60 48 69.5 68.9 43 119 61.1 58.3 73 36.1 32.4 85 120 38.6 34.2 54 32.6 28 7 121 73.9 68.9 39 85.9 80.9 63 122 30 30 94 68.9 68.8 26 123 56 51.3 17 81.3 78.6 53 124 39 36.1 72 52 50.4 104 125 7.4 3.5 81 60.4 58.2 67 126 74.9 74.5 16 23.9 19.4 43 127 40 37.9 43 59.6 55.8 28 128 43 39 23 44.5 44.3 54 129 28.8 24.6 67 90.8 88.8 67 130 14.5 10.5 14 66.5 63.5 11 131 10.8 9.9 59 60.8 56 19 132 6.6 1.9 12 83.6 82.5 8 133 12.6 10.7 51 35.6 33.7 41 134 3.4 0.2 86 81.4 78.5 45 135 40.6 40.6 30 8.6 3.7 12 136 67 63.5 70 7.2 6.3 35 137 33.6 32 97 80.6 75.7 44 138 67 66 59 3.5 3.2 84 139 14 9.5 94 52 49.4 24 140 22.7 19.7 34 6.7 2.7 18 141 69.6 65.6 26 54.6 49.6 65 142 68.7 65.2 38 11.7 8.5 13 143 70 68 95 84.7 82.7 83 144 57 54 89 57.9 57.1 103 145 56.6 54.6 89 22.6 18.3 97 146 69.4 69.2 80 85.4 80.9 77 147 81.7 77.3 86 72.7 70.8 22 148 70 65.8 72 30.3 28.5 57 149 39.3 37.2 52 10.3 6.2 108 150 16.8 13.3 49 80.8 80.1 11 151 65.3 62.5 19 64.3 59.6 100 152 15.9 14 91 31.9 29 84 153 57.5 54.8 72 70.5 66.5 45 154 55.7 55 61 7.7 5.7 71 155 67.3 63.5 39 20.3 16.5 54 156 10 9.6 72 56 52.3 77 157 96 94.1 81 6 2.1 46 158 57.7 55.7 22 24.7 23.7 75 159 15.7 15.2 77 59.7 55.4 35 160 12.2 7.8 94 53.2 48.8 13 161 56.1 52.5 58 48.1 47.8 24 162 10.3 9.6 36 19.3 16.3 64 163 58 54.7 98 6.3 3.5 61 164 7.5 6.5 59 26.5 22 84 165 14.4 12.8 62 44.4 43.7 59 166 57.5 57.4 46 89.5 89.2 36 167 40.1 39.7 68 69.1 67.5 49 168 23.3 21 33 48.3 44.7 103 169 59 57.9 53 89 84.4 108 170 24.2 19.3 33 56.2 54.6 20 171 62 59.2 22 30 25.1 67 172 45 40.7 37 57.8 56.3 42 173 42 42 33 70.4 68.5 16 174 60 59.5 54 50.1 46.5 43 175 77.8 75 32 18.8 15.9 63 176 73 70 76 24 22.2 103 177 13.4 12 53 38.4 35.5 16 178 29 27.9 57 73.6 71.5 93 179 97 92.7 31 25 24.7 60 180 10 7.7 62 19 18.5 70 181 21.7 19.5 13 49.7 49.6 47 182 42.9 41.1 69 67.9 63.2 107 183 23 20 42 28.6 28.3 50 184 35 34.7 15 26.7 24.2 40 185 3.4 3.3 34 51.4 47 25 186 45 40.6 72 53.5 53.1 99 187 7.9 4.6 50 6.9 2.2 23 188 44 41.2 63 9.1 6.2 97 189 8 3.1 36 70 68.3 83 190 33 31.9 27 17 13 106 191 2.6 2.4 63 57.6 55.6 87 192 24 23 63 19.2 17.8 52 193 23.6 19.7 30 34.6 32.2 46 194 49.1 45.3 67 57.1 54.2 37 195 1.5 1.3 69 80.5 80.4 98 196 57.4 52.8 89 81.4 80.4 108 197 60.9 59.8 56 69.9 69 88 198 59.7 56.1 65 16.7 14.9 106 199 1.8 1.7 20 78.8 75.4 7 200 63.1 61.7 40 54.1 52.2 57

Explanation / Answer

Solution1:

z score is x-mean/sd

|Z|>3 are outliers

Subtract each bvalue form mean

divide by stddev You will get Z score

Take the moduus of Z score

No outliers seen for

Domestic Cars_List Price in K(X).

No value is above 3

Domestic Cars_List Price in K Domestic Cars_Sale Price in K Domestic Cars_Days to Sell Mean 44.854 Mean 42.3965 Mean Median 49.3 Median 45.35 Median Standard Deviation 25.33192087 Standard Deviation 25.21323011 Standard Deviation Range 96.4 Range 95.7 Range Coefficientofvariation 56.47639201 Coefficientofvariation 59.47007444 Coefficientofvariation

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