MATH 533: Applied Managerial Statistics Course Project -Part A Charmaigne Obillo 15 July 2017 I. Introduction SALESCALL Inc. is a company with thousands of salespeople. Measures of central tendency are mean, median and mode. Measures dispersion is standard deviation, variance, range, IQR. Data includes 5 variables namely sales, calls, time, years and type. The data is used to determine the most productive sales person. With this information the company can conduct it's training to achieve the greatest number of sales. Their description is given below. SALES represents the number sales made this week. CALLS represents the number of sales calls made this week. TIME represents the average time per call this week. YEARS represents years of experience in the call center. TYPE represents the type of training the employee received. II. Individual Variables 1. Sales The descriptive statistics and boxplot for sales is given below. Sales (Y) Mean Standar d Error Median Mode Standar d Deviatio n Sample Variance Kurtosis Skewne ss Range Minimu m Maximu m Sum Count 42.55 0.71708 9 43 44 7.17089 4 51.4217 2 2.52254 4 0.10271 5 46 21 67 4255 100 Boxplot 20 30 40 50 60 70 Sales variable is skewed to the right. Sales have an average of 42.55 with standard deviation of 7.17. Median for sales is 45 implying half of the sales are less than 45 and other half is greater than 45. Median and IQR is considered as best measure of central tendency and variability when data is skewed. There are no outliers in the data of sales as evident from boxplot. Skewed data indicates that there is less frequency for high value of sales. 2. Calls The descriptive statistics and histogram for calls is given below. Calls (X1) Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 161.88 1.843431 160.5 178 18.43431 339.8238 -0.64306 -0.04928 81 120 201 16188 100 Calls 25 20 15 10 5 0 120-129 130-139 140-149 150-159 160-169 170-179 180-189 190-199 200-209 Calls variable is approximately normally distributed. Mean call is 161.88 with standard deviation of 18.43. The low value of standard deviation indicates that mean is trustworthy. empirical rule can be applied here which indicates that 68% of the data will fall within one standard deviation of the mean; 95% of the data will fall within two standard deviations of the mean; and 99.7% will fall within three standard deviations of the mean. 3. Years The descriptive statistics and histogram for Years is given below. Years (X3) Mean Standar d Error Median Mode Standar d Deviatio n Sample Variance Kurtosis Skewne ss Range Minimu m Maximu m Sum Count 2.3 0.14177 8 2 2 1.41778 2.01010 1 0.61042 0.34069 3 5 0 5 230 100 years 35 30 25 20 15 10 5 0 0 1 2 3 4 5 Years are slightly skewed to the right. Mode and median for years is 2. When data is skewed, median and IQR is the best measure of central tendency and dispersion respectively. From histogram and value of skewness I can say that there are very few frequencies with high value of years. III. Pairing of Variables 1. Sales and Calls The correlation coefficient for Sales and calls is .31. This indicates there is a weak positive linear relationship between Sales and calls. scatterplot 80 70 60 50 sales f(x) = 0.12x + 22.52 R = 0.1 40 30 20 10 0 110 120 130 140 150 160 170 180 190 200 210 calls An upward trend is observed between 2 variables and points are plotted not much close to each other. This implies as the value of call increases, the value of sales increases slightly. 2. Sales and Time The correlation coefficient between Sales and time is -.18. There is weak negative linear relationship between Sales and time. scatterplot 80 70 60 50 sales f(x) = - 0.58x + 51.44 R = 0.03 40 30 20 10 0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 time A downward trend is observed between 2 variables and relationship is weak as points are scattered away from each other. As the value of time increases, the value of sales decreases slightly. 3. Sales and Type The frequency distribution of Sales and type is given below along with pie chart. Row Labels GROUP NONE ONLINE Grand Total Count of Sales (Y) 30 20 50 100 Total 30% 50% GROUP NONE ONLINE 20% The count for online type of sales is highest with count 50. This is followed by group type with count of sales being 30. None type has lowest count of sales being only 20. The same ranks is observed from pie chart. IV. Conclusion Median for sales is 45 implying half of the sales are less than 45 and other half is greater than 45. Mean call is 161.88 with standard deviation of 18.43. The low value of standard deviation indicates that mean is trustworthy. Mode and median for years is 2. There are very few frequencies with high value of years. There is a weak positive linear relationship between Sales and calls. As the value of call increases, the value of sales increases slightly. There is weak negative linear relationship between Sales and time. As the value of time increases, the value of sales decreases slightly. The count for online type of sales is highest with count 50. This is followed by group type with count of sales being 30. None type has lowest count of sales being only 20. Sales (Y) 48 32 44 47 41 46 32 46 42 33 42 50 42 41 41 44 36 47 38 21 67 45 52 37 33 31 44 44 39 43 42 49 41 40 37 36 46 41 49 42 37 37 21 39 44 49 35 46 43 Calls (X1) 171 139 165 186 180 184 120 172 161 143 181 148 140 198 149 168 121 149 135 185 155 149 193 159 152 170 192 165 150 174 168 178 164 191 132 140 171 170 153 154 142 130 177 160 134 131 130 183 169 Time (X2) 13.0 16.9 15.7 13.5 14.0 12.7 19.9 14.7 13.2 15.4 11.5 16.0 17.5 13.2 17.3 11.0 18.0 15.8 18.5 18.9 17.9 13.5 13.7 18.1 15.0 14.3 16.7 12.4 15.3 12.7 16.4 15.1 17.8 19.0 10.0 15.7 14.9 12.3 19.0 14.3 13.9 16.9 17.0 14.3 19.4 14.6 19.4 15.4 14.0 Years (X3) 5 4 3 3 2 5 3 3 1 3 4 0 2 2 0 5 2 1 1 2 1 1 5 0 3 4 1 3 3 2 0 3 3 5 0 1 5 0 3 2 3 2 0 4 5 1 4 4 5 Type ONLINE NONE ONLINE ONLINE ONLINE ONLINE NONE GROUP GROUP NONE ONLINE NONE GROUP ONLINE ONLINE ONLINE NONE GROUP GROUP ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE GROUP ONLINE NONE NONE ONLINE ONLINE GROUP GROUP NONE NONE ONLINE NONE GROUP GROUP NONE ONLINE GROUP 41 48 39 40 48 50 44 43 33 32 46 48 56 44 34 43 33 49 50 52 45 48 35 44 44 67 51 41 40 45 41 40 47 48 42 41 29 48 33 48 45 36 43 42 49 50 42 44 45 48 39 155 182 140 157 167 144 168 175 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 138 159 145 151 186 194 152 145 188 139 201 156 131 161 152 178 157 154 156 170 170 144 16.0 13.0 12.4 15.4 14.8 15.8 12.4 13.6 14.9 17.9 16.6 14.5 15.0 15.3 14.2 10.9 17.5 18.3 14.3 11.4 13.6 13.6 15.6 14.6 14.8 18.9 16.5 13.4 12.6 15.3 18.8 14.7 16.6 14.2 13.6 14.5 19.0 11.3 19.3 12.5 13.2 18.5 17.3 14.6 16.4 15.9 15.3 20.0 14.2 17.4 17.7 2 2 1 1 3 2 2 5 2 1 2 4 3 2 3 4 1 2 1 4 2 0 1 2 2 1 1 2 1 2 2 2 2 1 2 4 2 2 3 1 3 2 3 1 2 3 1 0 1 5 3 ONLINE ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE ONLINE ONLINE GROUP ONLINE ONLINE ONLINE ONLINE GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE NONE ONLINE NONE GROUP ONLINE ONLINE GROUP NONE ONLINE GROUP ONLINE GROUP NONE ONLINE ONLINE ONLINE GROUP GROUP ONLINE ONLINE ONLINE NONE Boxplot 3 2 1 20 30 40 50 60 70 Sales (Y) Calls (X1) Mean Standard Error Median Mode Standard Devia Sample Varianc Kurtosis Skewness Range Minimum Maximum Sum Count Time (X2) 42.55 Mean 161.88 Mean 0.717089375 Standard Error 1.843431 Standard Error 43 Median 160.5 Median 44 Mode 178 Mode 7.1708937499 Standard Deviati 18.43431 Standard Deviati 51.4217171717 Sample Variance 339.8238 Sample Variance 2.5225437971 Kurtosis -0.643056 Kurtosis 0.1027145321 Skewness -0.049276 Skewness 46 Range 81 Range 21 Minimum 120 Minimum 67 Maximum 201 Maximum 4255 Sum 16188 Sum 100 Count 100 Count 15.338 0.229988 15.05 14.3 2.299881 5.289451 -0.639972 0.102994 10 10 20 1533.8 100 Years (X3) Sum - Years (X3) 0 0 1 22 2 58 3 60 4 40 5 50 Total Result 230 years 250 200 150 100 50 0 0 1 2 3 4 5 Total Result Years (X3) Calls (X1) Sum - Calls (X1) 120-129 241 130-139 1339 140-149 2027 150-159 3247 160-169 2627 170-179 3133 180-189 2405 190-199 968 200-209 201 Total Result 16188 Mean 2.3 Standard Er0.141778 Median 2 Mode 2 Standard D 1.41778 Sample Var 2.010101 Kurtosis -0.610422 Skewness 0.340693 Range 5 Minimum 0 Maximum 5 Sum 230 Count 100 Calls 18000 16000 14000 12000 10000 8000 6000 4000 2000 0 Type Count - Sales (Y) GROUP 30 NONE 20 ONLINE 50 Total Result 100 Total 15% 10% 50% 25% GROUP NONE ONLINE Total Result Calls (X1) Sales (Y) 171 48 139 32 0.318075 165 44 186 47 180 41 184 46 120 32 172 46 161 42 143 33 181 42 148 50 140 42 198 41 149 41 168 44 121 36 149 47 135 38 185 21 155 67 149 45 193 52 159 37 152 33 170 31 192 44 165 44 150 39 174 43 168 42 178 49 164 41 191 40 132 37 140 36 171 46 170 41 153 49 154 42 142 37 130 37 177 21 160 39 134 44 131 49 130 35 183 46 169 43 155 41 182 48 140 39 157 40 167 48 144 50 168 44 175 43 scatterplot 80 70 60 50 sales f(x) = 0.1237301799x + 22.52055 R = 0.1011715851 40 30 20 10 0 110 120 130 140 150 160 calls 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 138 159 145 151 186 194 152 145 188 139 201 156 131 161 152 178 157 154 156 170 170 144 33 32 46 48 56 44 34 43 33 49 50 52 45 48 35 44 44 67 51 41 40 45 41 40 47 48 42 41 29 48 33 48 45 36 43 42 49 50 42 44 45 48 39 scatterplot = 0.1237301799x + 22.5205584831 0.1011715851 130 140 150 160 calls 170 180 190 200 210 Time (X2) Sales (Y) 13.0 48 16.9 32 -0.185879 15.7 44 13.5 47 14.0 41 12.7 46 19.9 32 14.7 46 13.2 42 15.4 33 11.5 42 16.0 50 17.5 42 13.2 41 17.3 41 11.0 44 18.0 36 15.8 47 18.5 38 18.9 21 17.9 67 13.5 45 13.7 52 18.1 37 15.0 33 14.3 31 16.7 44 12.4 44 15.3 39 12.7 43 16.4 42 15.1 49 17.8 41 19.0 40 10.0 37 15.7 36 14.9 46 12.3 41 19.0 49 14.3 42 13.9 37 16.9 37 17.0 21 14.3 39 19.4 44 14.6 49 19.4 35 15.4 46 14.0 43 16.0 41 13.0 48 12.4 39 15.4 40 14.8 48 15.8 50 12.4 44 13.6 43 scatterplot 80 70 60 50 sales f(x) = - 0.5795603064x + 51.43929598 R = 0.0345510499 40 30 20 10 0 8.0 10.0 12.0 14.0 16.0 time 18.0 14.9 17.9 16.6 14.5 15.0 15.3 14.2 10.9 17.5 18.3 14.3 11.4 13.6 13.6 15.6 14.6 14.8 18.9 16.5 13.4 12.6 15.3 18.8 14.7 16.6 14.2 13.6 14.5 19.0 11.3 19.3 12.5 13.2 18.5 17.3 14.6 16.4 15.9 15.3 20.0 14.2 17.4 17.7 33 32 46 48 56 44 34 43 33 49 50 52 45 48 35 44 44 67 51 41 40 45 41 40 47 48 42 41 29 48 33 48 45 36 43 42 49 50 42 44 45 48 39 plot + 51.43929598 time 16.0 18.0 20.0 22.0 Part B: Hypothesis Testing and Confidence Intervals Complete the following four hypotheses, using = 0.05 for each. a. Mean sales per week exceeds 41.5 per salesperson b. Proportion receiving online training is less than 55% c. Mean calls made among those with no training is less than 145 d. Mean time per call is greater than 15 minutes 1. Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager's belief. Use the Seven Elements of a Test of Hypothesis from Section 7.1 of your text book, as well as the p-value calculation from Section 7.3, and explain your conclusion in simple terms. 2. Compute 99% confidence intervals for each of the variables described in a.-d., and interpret these intervals. 3. Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. 4. All DeVry University policies are in effect, including the plagiarism policy. 5. Project Part B report is due by the end of Week 6. 6. Project Part B is worth 100 total points. See grading rubric below. Format for report: A. B. Summary Report (about one paragraph on each of the speculations a.- d.) Appendix with the calculations of the Seven Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas used in the calculations. Part B: Grading Rubric Category Point s % Description Addressing each speculation20 80 80 Hypothesis test, interpretation, confidence Category Point s % points each Description interval, and interpretation Summary report clarity 20 20 One paragraph on each of the speculations Total 100 10 0 A quality paper will meet or exceed all of the above requirements