The following report presents the detailed statistical analysis of the data collected from a sample of credit customers in the department chain store AJ DAVIS. The 1st individual variable considered is Location. It is a categorical variable. The three subcategories are Urban, Suburban and Rural. Since this is a categorical variable, the measures of central tendency and descriptive statistics has not been calculated for this variable. The frequency distribution and pie chart are given as follows: Frequency Distribution: Location Frequency Urban 21 Suburban 15 Rural 14 From the frequency distribution and pie chart, it is evident that the maximum number of customers belongs to the rural category (42%), followed by those in the suburban category (30%). Only 28% of the customers belong to the urban category. The 2nd individual variable considered is Size. It is a quantitative variable. The measures of central tendency, variation and other descriptive statistics have been calculated for this variable and are given as follows: Descriptive Statistics: Size Mean 3.42 Standard Error 0.24593014 Median 3 Mode 2 Standard Deviation 1.73898868 Sample Variance 3.02408163 Kurtosis Skewness Range Minimum Maximum Sum Count Size 1 2 3 4 5 6 7 -0.7228086 0.52789598 6 1 7 171 50 Frequency Distribution: Frequency 5 15 8 9 5 5 3 The mean household size of the customers is given as 3.42. The median of the data is 3 and the mode is 2. The standard deviation is given approximately as 1.74. Maximum number of customers has a household size of 2 as is evident from the frequency distribution and the bar graph. The 3rd individual variable considered is Credit Balance. It is a quantitative variable. The measures of central tendency, variation and other descriptive statistics have been calculated for this variable and are given as follows: Descriptive Statistics: Credit Balance($) Mean 3964.06 Standard Error 132.0159991 Median 4090 Mode 3890 Standard Deviation 933.4940816 Sample Variance 871411.2004 Kurtosis -0.741830067 Skewness -0.129506489 Range 3814 Minimum 1864 Maximum 5678 Sum 198203 Count 50 Relative Frequency Distribution: Credit Balance ($) Frequency Relative Frequency 1500 - 2000 1 0.02 2000 - 2500 2 0.04 2500 - 3000 6 0.12 3000 - 3500 6 0.12 3500 - 4000 8 0.16 4000 - 4500 12 0.24 4500 - 5000 7 0.14 5000 - 5500 6 0.12 5500 - 6000 2 0.04 The mean credit balance of the customers is given as $3964.06. The standard deviation is given approximately as 933.49. The credit balance of the customers is more or less normally distributed with the peak of the bell shaped distribution lying in the range $4000 - $4500. Thus, maximum number of customers has a credit balance within this range. The relationship between the variables Income and Size is illustrated in the following scatter plot: As is evident from the scatter plot, there is no definite relationship or association between the two variables. The points are haphazard and do not exhibit any specific pattern. In other words, there is no correlation among the variables Income and Size. The relationship between the variables Income and Credit Balance is illustrated in the following scatter plot: As is evident from the scatter plot, there is a clear and definite relationship between the two variables. The variables Income and Credit Balance exhibit a linear positive relationship or correlation. If Income increases, Credit Balance also increases or vice versa. The relationship between the variables Years and Credit Balance is illustrated in the following scatter plot: As is evident from the scatter plot, these two variables do not show any clear relationship. The points are haphazard and do not exhibit any specific pattern. In other words, there is significant correlation among the variables Years and Credit Balance. We can conclude that, though not all, but some of the variables like Income etc. are strongly conclusive of the Credit Balance of the customers in the respective department store. \f\fSales (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 48 155 182 140 157 167 144 168 175 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 138 159 145 151 186 194 152 145 188 139 201 156 131 161 152 178 157 154 156 170 170 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 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 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 39 144 17.7 3 NONE Name:_____________________________ Project Part B Answer the following questions using the data in a the AJ case file (the data set you already have in your course file) Answer A-D A. The Manager of AJ believe the average (mean) annual income of customers was less than $50,000. Using the data set annual income, is there convincing evidence that the true mean annual salary is less than $50,000 ? Use =.05. 1. Null hypothesis (Ho): 2. Alternative (research) hypothesis (Ha): 3. Test statistic: 4. Rejection region: 5. Assumptions: 6. Conclusion B. Is the true population proportion of customers who live in an urban area exceeds 40% 1. Null hypothesis (Ho): 2. Alternative (research) hypothesis (Ha): 1 Name:_____________________________ Project Part B 3. Test statistic: 4. Rejection region: 5. Assumptions: 6. Experiment and calculation of test statistic: 7. Conclusion: C. The AJ manager assumed average (mean) number of years lived in the current home is less than 13 years. Is this assumption correct? Choose alpha. (ii) Additionally, calculate a 95% confidence interval for this tests statistic value. 1. 2. 3. 4. 5. 6. Null hypothesis (Ho): Alternative (research) hypothesis (Ha): Test statistic: Rejection region: Assumptions: Experiment and calculation of test statistic: ( 2 Name:_____________________________ Project Part B 7. Conclusion: D. Is the average (mean) credit balance for suburban customers is more than $4300? Choose your own alpha and test the hypothesis. (ii) Additionally, calculate a 95% confidence interval for this tests statistic value. 1. 2. 3. 4. 5. Null hypothesis (Ho): Alternative (research) hypothesis (Ha): Test statistic: Rejection region: Assumptions: 3 Name:_____________________________ Project Part B 6. Experiment and calculation of test statistic: 7. Conclusion: 4 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 48 155 182 140 157 167 144 168 175 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 138 159 145 151 186 194 152 145 188 139 201 156 131 161 152 178 157 154 156 170 170 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 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 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 39 144 17.7 3 NONE Name:_____________________________ Project Part B Answer the following questions using the data in a the AJ case file (the data set you already have in your course file) Answer A-D A. The Manager of AJ believe the average (mean) annual income of customers was less than $50,000. Using the data set annual income, is there convincing evidence that the true mean annual salary is less than $50,000 ? Use =.05. 1. Null hypothesis (Ho): 2. Alternative (research) hypothesis (Ha): 3. Test statistic: 4. Rejection region: 5. Assumptions: 6. Conclusion B. Is the true population proportion of customers who live in an urban area exceeds 40% 1. Null hypothesis (Ho): 2. Alternative (research) hypothesis (Ha): 1 Name:_____________________________ Project Part B 3. Test statistic: 4. Rejection region: 5. Assumptions: 6. Experiment and calculation of test statistic: 7. Conclusion: C. The AJ manager assumed average (mean) number of years lived in the current home is less than 13 years. Is this assumption correct? Choose alpha. (ii) Additionally, calculate a 95% confidence interval for this tests statistic value. 1. 2. 3. 4. 5. 6. Null hypothesis (Ho): Alternative (research) hypothesis (Ha): Test statistic: Rejection region: Assumptions: Experiment and calculation of test statistic: ( 2 Name:_____________________________ Project Part B 7. Conclusion: D. Is the average (mean) credit balance for suburban customers is more than $4300? Choose your own alpha and test the hypothesis. (ii) Additionally, calculate a 95% confidence interval for this tests statistic value. 1. 2. 3. 4. 5. Null hypothesis (Ho): Alternative (research) hypothesis (Ha): Test statistic: Rejection region: Assumptions: 3 Name:_____________________________ Project Part B 6. Experiment and calculation of test statistic: 7. Conclusion: 4