duction In this analysis we first examined the general attitude of shoppers toward each shopping area. We found that the point estimate of the population mean attitude toward the Springdale shopping mall was 4.09, which means that shoppers generally like the Springdale Mall. The confidence interval was (3.94, 4.23), and the maximum likely error in the estimate of the population mean was found to be 0.14. We also found that the point estimate of the population mean attitude toward the Downtown shopping mall was 3.52, which means that shoppers attitudes toward the Downtown Mall was between neutral and like. The confidence interval was (3.35, 3.69), and the maximum likely error in the estimate of the population mean was found to be 0.17. For the West Mall, we found that the point estimate of the population mean attitude toward the West mall was 3.25, which means that shoppers attitudes toward the Downtown Mall was between generally neutral. The confidence interval was (3.05, 3.44), and the maximum likely error in the estimate of the population mean was found to be 0.19. We also constructed a 95% confidence interval for the population proportion of males and found that the 95% confidence interval for pi 26= the population proportion of males is: (0.309, 0.456). Finally, we constructed a 95% confidence interval for the population proportion of single or other, and found that the 95% confidence interval for pi 28= the population proportion of single or other is: (0.474, 0.633). 1. For u7: Springdale Mall Average T Std Dev LCL UCL e CI : x t 4.09 2.26 0.78 3.94 4.23 0.14 s n LCL 4.09 2.26 * UCL 4.09 2.26 * 95% CI : (3.94, 4.23) 0.78 150 0.78 150 3.94 4.23 e t * s n e 2.26 * 0.78 250 e 0.14 Maximum likely error in the estimate of the population mean = 0.14 2. For u8: Downtown Mall Average T Std Dev LCL UCL e CI : x t 3.52 2.26 0.94 3.35 3.69 0.17 s n LCL 3.52 2.26 * UCL 3.52 2.26 * 0.94 150 0.94 150 3.35 3.69 95% CI: (3.35, 3.69) e t * s n e 2.26 * 0.94 250 e 0.17 Maximum likely error in the estimate of the population mean = 0.17 For u9: West Mall Average T Std Dev LCL UCL e CI : x t 3.25 2.26 1.04 3.05 3.44 0.19 s n LCL 3.25 2.26 * UCL 3.52 2.26 * 1.04 150 1.04 150 3.05 3.44 95% CI: (3.05, 3.44) e t * s n e 2.26 * 1.04 250 e 0.19 Maximum likely error in the estimate of the population mean = 0.19 3. Variable 26: Gender Males Females Total p Z LCL UCL e 58 92 150 0.387 1.960 0.309 0.465 0.078 58 p 0.387 150 p * (1 p ) CI : p Z * n LCL 0.387 1.96 * 0.387 * (1 0.387) 0.309 150 UCL 0.387 1.96 * 0.387 * (1 0.387) 0.465 150 The 95% confidence interval for pi 26= the population proportion of males is: (0.309, 0.456) e 1.96 * 0.387 * (1 0.387) 150 e 0.078 The maximum likely error in the point estimate of the population proportion is 0.078 4. Married Single or Other Total p Z LCL UCL e 67 83 150 0.553 1.960 0.474 0.633 0.080 83 p 0.553 150 p * (1 p) CI : p Z * n LCL 0.553 1.96 * 0.553 * (1 0.553) 0.474 150 UCL 0.553 1.96 * 0.553 * (1 0.553) 0.633 150 The 95% confidence interval for pi 28= the population proportion of single or other is: (0.474, 0.633) e 1.96 * 0.553 * (1 0.553) 150 e 0.080 The maximum likely error in the point estimate of the population proportion is 0.080 Conclusion In conclusion, we have seen that shoppers generally like to shop at the Sprindale Mall, whereas their attitude toward the Downtown Mall is between neutral and like. The attitude of shoppers toward the West Mall is generally neutral. We also found that we can be 95% confident that the population proportion of males is less than the population proportion of females. In other words, the number of female shoppers exceeds the number of male shoppers. Finally, we found that the population proportion of shoppers in the single or other category is not significantly different from the population proportion of shoppers in the married category. This is because we found that the 95% confidence interval for pi 28= the population proportion of single or other is: (0.474, 0.633), which implies that there could very well be equal proportions of married vs single or other shoppers (ie 50 - 50 split is possible). A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 B C D E F SPRIFREQ DOWNFREQ WESTFREQ SPRSPEND DOWSPEND WESSPEND 5 5 5 6 7 7 4 6 6 6 7 7 6 5 6 7 7 7 6 4 6 5 7 7 4 6 3 6 7 6 5 5 4 7 6 7 5 4 5 6 7 7 4 5 4 5 7 7 3 5 2 4 5 7 5 6 6 7 7 7 6 4 6 7 6 7 5 4 5 7 7 7 6 3 5 6 6 7 4 6 5 6 7 7 4 5 2 5 6 7 6 4 6 7 7 7 6 5 6 7 7 7 6 4 5 7 7 7 6 5 6 6 6 7 3 5 6 6 7 7 5 4 5 7 7 7 5 6 5 5 7 7 5 5 5 6 7 7 6 4 3 7 6 7 5 4 6 5 7 6 6 5 5 7 7 7 5 6 6 4 7 7 3 6 5 6 6 7 5 3 2 5 7 6 6 4 5 6 7 7 6 5 6 6 7 7 6 4 4 6 7 7 6 3 4 7 7 7 6 5 5 6 7 7 4 5 6 7 7 7 5 4 5 7 6 7 2 6 4 4 7 5 3 4 5 7 6 7 3 6 5 5 7 5 6 6 5 6 6 7 4 6 4 5 7 3 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 A B C D E F 4 6 4 5 5 5 3 3 2 4 4 5 5 3 3 3 1 2 5 6 3 2 6 4 3 5 1 2 2 2 3 4 4 1 5 1 6 1 1 3 1 5 4 3 6 6 2 2 6 2 6 1 6 4 3 4 5 3 2 5 2 2 4 6 5 5 5 2 5 2 4 3 4 4 1 6 4 2 4 2 4 2 6 2 4 6 5 6 3 5 5 3 3 2 3 1 3 5 6 6 3 1 1 6 1 4 6 3 1 5 6 3 3 2 5 4 2 2 5 6 3 4 3 6 4 3 6 7 5 6 6 6 6 2 2 5 2 7 3 4 4 6 1 2 7 6 7 4 7 2 4 6 5 6 2 4 5 7 2 5 1 5 5 2 1 6 4 1 6 5 5 6 7 6 7 4 7 1 7 3 6 2 3 3 3 2 1 2 7 1 1 6 5 6 1 5 2 4 3 7 1 1 1 2 3 7 5 1 1 3 3 7 6 7 4 6 7 6 7 4 6 2 3 2 1 1 6 2 2 5 1 6 2 2 7 6 2 4 1 3 7 2 5 7 6 4 2 5 2 4 6 3 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 A B C D E F 1 2 4 3 4 2 3 6 5 1 2 5 2 2 6 6 6 2 2 5 5 6 6 4 5 3 3 2 3 4 5 5 6 3 5 4 5 3 3 1 4 4 2 1 1 5 1 3 2 3 6 6 2 5 1 3 6 5 4 1 5 4 1 6 6 6 5 5 6 4 5 4 5 3 5 5 4 4 3 4 6 6 5 6 6 4 2 5 2 4 1 6 6 3 2 5 1 3 6 6 6 4 5 5 5 6 6 5 6 4 4 3 4 4 5 4 6 6 6 5 3 6 5 6 6 5 6 2 5 6 4 5 2 1 7 5 7 2 3 2 7 4 5 4 7 5 3 4 6 5 7 7 7 5 7 7 7 6 6 7 4 4 6 5 6 6 4 5 1 6 3 7 2 4 3 1 5 4 3 7 3 1 7 6 6 7 6 5 7 5 6 7 7 7 7 6 7 6 6 7 7 7 5 5 7 5 6 7 6 7 7 1 2 5 2 4 7 4 6 6 6 3 4 6 7 5 5 6 5 5 4 6 6 6 7 7 5 5 7 7 7 7 7 7 7 5 7 7 7 7 7 6 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 A B C D E F 5 5 5 4 5 3 5 5 2 5 5 5 5 4 1 5 6 2 5 4 6 3 3 6 6 6 5 3 5 5 4 3 6 6 4 5 6 3 5 5 1 5 4 3 3 5 6 4 6 1 6 2 5 3 1 4 6 4 5 3 3 4 6 3 1 2 5 5 4 5 5 4 4 6 4 5 7 4 5 6 7 7 6 5 4 6 7 7 7 4 5 6 7 5 7 7 6 7 4 7 5 7 4 5 7 7 7 6 7 7 7 7 7 6 6 4 7 7 5 7 7 6 6 5 6 6 7 6 5 7 7 7 7 5 6 6 5 7 7 6 4 6 6 7 7 7 6 7 4 5 G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 H I J K L M SPRILIKE DOWNLIKE WESTLIKE BSTEXCHG BSTQUALI BSTPRICE BSTVARIE 4 4 4 1 1 3 1 5 4 3 1 1 3 1 5 3 4 3 4 4 1 2 4 3 4 2 4 1 3 3 3 1 1 1 1 5 5 3 1 1 3 1 4 2 4 1 1 3 1 4 3 3 2 2 3 1 5 4 4 3 2 3 1 4 4 3 1 1 1 1 3 3 3 4 4 3 1 3 4 3 1 2 3 1 3 4 3 4 1 3 2 3 2 3 4 1 4 1 4 3 4 1 1 3 3 4 3 2 1 1 1 1 4 4 4 4 1 3 1 4 4 3 3 1 3 1 4 4 3 1 2 3 1 4 3 1 1 1 2 1 4 3 2 1 4 4 1 4 3 3 4 1 2 1 5 3 4 1 1 3 1 2 5 4 2 2 2 1 4 3 2 1 1 3 1 4 4 4 1 1 2 1 4 3 3 1 1 3 1 4 4 4 1 1 3 1 4 4 5 1 1 1 1 3 5 3 4 2 3 1 4 4 3 1 1 1 1 4 4 4 4 2 3 1 5 3 3 1 1 3 1 3 3 2 1 1 3 1 4 4 3 4 1 1 1 4 5 4 2 2 2 2 5 3 4 1 1 3 1 4 3 3 1 2 3 1 3 2 1 1 1 4 1 4 4 4 3 2 3 1 4 3 4 1 1 3 1 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 G H I J K L M 5 3 4 4 4 4 5 3 4 4 4 4 2 1 5 1 3 1 3 2 4 3 4 5 5 3 3 2 4 1 3 2 2 5 1 4 5 3 4 5 4 4 5 5 2 3 4 4 1 2 3 3 1 5 4 4 5 4 5 2 5 2 5 3 4 1 1 3 2 4 1 5 3 5 2 1 5 1 4 3 1 5 5 3 5 3 4 3 4 3 4 3 5 5 4 1 1 5 4 5 3 3 2 5 4 1 5 5 3 3 4 5 5 5 5 4 3 1 2 4 1 5 2 3 1 4 1 2 1 2 3 4 4 2 2 4 4 1 1 4 1 1 1 2 3 1 2 2 1 2 4 1 1 2 3 3 1 1 2 3 1 1 3 4 1 4 2 3 1 2 1 2 1 2 1 3 4 4 4 1 1 3 4 1 4 3 4 3 1 3 2 3 1 4 2 4 1 3 3 3 3 1 2 4 1 1 4 4 4 1 3 2 3 3 3 4 4 1 1 2 2 2 2 1 3 1 4 2 3 3 3 4 3 3 3 1 1 3 4 3 3 3 1 1 1 4 2 4 2 4 4 3 1 2 2 2 1 4 1 2 2 1 4 3 4 3 3 2 3 1 4 3 1 1 4 1 1 3 4 1 1 4 4 3 2 4 1 3 3 4 2 3 4 4 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 G H I J K L M 5 5 2 3 1 3 4 2 2 2 4 5 3 4 5 4 5 5 5 4 4 4 4 4 4 5 4 5 4 5 4 5 5 5 5 4 4 4 4 4 3 5 4 2 4 1 5 2 2 4 3 1 3 4 1 4 4 3 4 3 3 4 3 4 4 2 3 3 3 3 3 4 5 3 4 4 4 4 4 5 3 4 3 2 5 1 4 4 4 5 1 2 2 4 4 4 1 3 3 3 4 3 3 4 5 4 5 3 1 4 4 1 4 4 3 4 2 2 3 3 2 1 1 1 3 4 3 4 3 4 4 1 1 2 4 3 3 4 4 2 1 2 3 2 2 4 2 2 1 1 4 4 4 1 1 1 1 3 4 1 1 1 1 1 1 1 1 1 2 2 4 2 4 1 4 2 4 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 2 1 1 1 1 4 3 2 3 3 1 3 4 1 1 1 3 2 1 3 3 3 3 3 3 2 3 3 1 3 3 3 3 1 3 3 1 2 2 3 3 1 3 3 3 1 3 4 2 1 1 2 4 2 3 3 3 1 2 4 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 G H I J K L M 4 3 4 4 3 3 5 5 5 5 5 4 3 4 4 4 5 5 5 5 1 4 5 5 3 3 4 3 4 4 3 5 4 3 1 3 3 5 4 3 5 4 4 5 4 5 3 3 2 5 3 5 3 4 4 3 2 5 3 4 4 5 3 2 2 4 4 4 5 2 1 4 4 3 3 4 4 4 3 3 1 2 1 1 3 3 3 2 1 4 3 4 1 1 1 2 1 1 4 2 2 4 2 4 1 4 2 2 1 1 1 2 1 1 2 3 1 1 1 1 2 2 2 1 2 3 3 3 3 1 4 2 2 3 3 3 3 2 3 3 3 3 3 3 3 3 1 1 4 3 1 4 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 2 1 1 1 2 N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 O P Q R S T BSTHELP BSTHOURS BSTCLEAN BSTBARGN IMPEXCH IMPQUALI IMPPRICE 1 1 1 1 6 7 7 2 3 1 3 7 7 7 1 4 1 1 7 7 7 4 1 1 4 6 7 7 1 1 1 2 7 7 7 1 1 1 3 3 7 7 2 1 1 3 4 6 7 4 1 1 3 7 7 7 1 1 4 1 7 5 5 1 1 1 1 7 7 7 2 4 4 3 5 7 7 1 1 1 3 5 6 6 4 1 1 1 7 7 7 4 1 1 2 7 7 7 1 3 1 3 7 7 7 2 1 1 4 1 4 4 4 4 1 3 2 7 7 3 3 1 3 7 7 7 2 2 1 2 7 7 7 1 1 1 2 1 1 1 4 1 1 4 3 4 5 4 1 1 2 6 6 6 1 1 1 1 5 6 7 2 1 1 2 5 6 1 1 1 1 4 5 7 7 2 1 1 1 1 1 1 1 1 1 1 7 7 7 2 1 1 1 7 6 7 4 1 1 3 4 7 7 2 1 4 4 5 7 7 1 1 1 2 5 7 7 4 4 3 3 3 7 7 4 1 1 1 7 7 7 2 1 1 2 5 7 7 2 2 1 2 1 1 7 2 2 1 2 6 7 7 1 1 1 1 7 7 7 1 3 1 1 6 6 7 4 1 1 1 7 7 7 4 3 2 4 7 7 7 4 1 1 3 4 7 7 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 N O P Q R S T 1 2 1 2 2 4 4 4 1 3 2 1 3 1 4 2 1 1 4 1 2 3 1 3 1 3 4 1 2 1 3 3 2 1 2 1 2 3 3 2 4 4 1 2 1 1 1 1 1 4 3 3 2 3 3 4 2 2 3 2 4 2 1 1 3 1 1 1 1 2 4 1 1 4 4 3 2 4 2 3 3 2 2 1 1 2 1 1 1 4 1 4 4 2 1 2 3 3 1 4 1 2 3 3 3 1 1 2 3 3 3 1 3 4 2 1 4 3 1 3 3 2 4 3 1 1 3 2 1 3 2 4 1 3 3 1 4 2 3 4 2 3 3 1 1 3 3 4 1 2 1 1 4 4 2 4 3 1 2 1 3 2 4 1 2 1 4 3 7 3 6 7 5 1 6 3 3 6 4 7 7 7 5 6 3 7 3 4 1 4 1 7 6 1 2 7 2 3 2 6 5 3 1 4 3 1 7 2 5 4 7 7 5 6 7 7 7 2 6 3 6 5 3 6 7 5 4 6 7 5 6 3 3 7 3 6 2 5 1 1 7 4 7 4 6 2 3 4 5 4 5 4 7 7 7 7 7 7 7 1 2 1 2 5 3 7 7 4 7 4 1 4 6 1 4 7 4 7 2 7 7 4 2 7 4 2 6 5 2 3 4 7 5 6 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 N O P Q R S T 3 2 2 4 4 4 3 4 4 2 1 2 1 4 1 1 1 1 2 1 2 1 1 1 1 4 3 1 4 2 2 2 1 2 2 1 1 2 1 1 1 1 3 4 2 1 1 4 1 3 4 2 3 4 2 2 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 3 1 1 1 4 1 1 3 2 2 3 4 4 3 4 4 3 1 4 3 1 2 3 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 4 4 1 4 1 4 4 3 4 4 2 4 3 2 1 3 3 2 3 3 1 3 1 1 3 4 4 4 1 1 2 1 2 3 1 3 1 1 2 3 1 1 4 5 5 6 1 4 6 5 1 6 4 4 7 6 7 6 4 5 6 2 5 3 5 7 3 5 5 7 7 7 6 5 4 7 7 7 7 4 7 7 6 7 6 7 2 6 6 1 5 6 7 5 6 1 6 4 6 6 7 3 7 7 7 7 5 7 7 6 7 7 5 7 7 7 7 7 7 7 7 7 6 7 7 7 1 7 6 2 5 6 2 5 4 6 4 5 6 2 7 6 6 4 5 6 7 7 6 7 7 7 7 4 7 7 7 7 7 5 7 7 6 6 7 3 7 7 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 N O P Q R S T 4 4 1 4 1 4 2 1 1 3 3 3 1 1 1 1 1 1 1 1 2 4 1 3 2 4 4 1 3 4 1 1 3 1 1 3 3 1 1 3 2 1 1 1 1 3 1 1 1 3 4 1 1 1 1 4 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 4 1 1 2 1 3 2 3 1 1 2 2 3 1 3 3 2 3 3 2 3 1 1 2 3 1 1 3 3 7 1 1 7 7 5 6 7 7 6 2 7 3 7 2 7 6 7 7 5 7 7 3 3 7 7 4 1 5 7 3 7 7 7 6 6 6 5 6 7 7 7 7 7 7 7 7 4 7 7 7 5 7 7 7 4 7 7 5 7 7 7 6 7 7 7 7 7 4 7 7 7 5 7 4 U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 V W X Y Z AA IMPVARIE IMPHELP IMPHOURS IMPCLEAN IMPBARGN RESPGEND RESPEDUC 6 5 6 6 7 2 3 7 7 7 7 6 2 3 5 4 5 3 7 1 3 6 6 5 6 7 2 3 7 7 7 7 7 2 3 6 5 6 5 6 2 3 5 3 6 4 5 2 1 6 7 7 7 7 2 3 7 6 7 7 6 1 4 7 7 7 7 7 2 4 5 5 4 4 5 2 3 5 5 6 6 7 2 1 6 4 4 6 5 2 3 7 7 7 5 6 2 3 6 4 6 3 6 1 3 6 2 3 4 1 1 3 6 4 3 3 6 2 4 7 4 4 3 6 2 3 7 5 6 6 5 2 3 1 1 1 1 1 2 3 4 6 4 4 5 1 4 6 5 7 6 7 1 4 7 2 5 3 6 2 3 1 6 1 6 5 1 3 6 6 5 6 7 2 3 2 3 2 4 3 1 3 5 5 4 7 4 1 3 6 6 6 5 6 1 3 5 5 7 7 7 1 3 6 4 2 3 5 2 3 5 5 4 4 5 1 3 6 7 6 6 6 2 3 7 7 7 5 7 2 3 7 6 5 5 6 2 3 7 6 7 2 7 2 3 6 6 3 5 6 1 3 7 7 7 7 4 2 3 3 5 5 7 4 1 4 7 4 7 7 7 2 4 7 4 7 7 7 2 2 5 4 6 4 7 2 2 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 U V W X Y Z AA 5 3 6 6 6 5 6 7 6 1 7 7 7 6 6 4 4 3 4 5 2 7 3 3 7 5 2 3 7 7 4 4 7 5 1 2 5 1 7 2 3 7 3 1 4 7 5 3 6 7 7 4 1 1 5 1 7 7 2 7 7 3 3 7 7 3 5 3 6 7 7 2 1 5 3 3 5 5 1 3 5 7 4 7 5 2 6 6 7 3 5 5 4 5 4 3 2 7 4 5 3 4 6 3 3 4 3 5 5 3 4 4 7 7 6 5 6 1 1 1 4 3 6 1 4 3 5 3 5 7 6 3 7 7 2 5 2 6 4 7 4 2 2 1 5 4 2 6 3 3 4 1 4 1 7 2 2 1 1 4 6 2 3 7 2 2 2 3 4 7 5 5 7 5 7 6 2 5 3 6 5 5 7 2 5 5 4 6 6 2 7 3 3 1 2 7 7 7 7 2 7 5 3 7 4 3 4 2 3 2 2 1 2 1 2 1 2 1 2 2 2 1 1 2 1 2 2 2 2 1 1 2 2 1 1 1 2 1 1 1 1 2 2 1 1 2 2 2 1 1 2 1 4 4 3 3 4 4 2 2 1 2 3 4 2 2 2 4 2 2 4 1 4 1 4 4 4 1 4 1 4 2 1 3 2 3 4 1 2 1 1 2 2 2 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 U V W X Y Z AA 2 2 3 4 1 3 5 3 7 2 7 7 3 1 7 7 7 3 7 7 6 6 5 5 6 4 6 4 5 7 6 7 4 7 4 7 5 7 7 7 6 7 1 4 4 7 1 1 4 6 6 2 4 3 7 1 7 6 6 1 6 5 4 2 3 6 7 4 7 7 6 7 6 7 3 6 1 6 7 5 7 7 4 7 2 3 7 5 2 2 2 4 2 2 5 4 3 6 7 6 6 1 6 3 6 5 4 6 5 7 5 6 6 7 6 5 6 7 7 7 6 7 6 7 6 6 7 4 3 7 6 6 3 4 4 6 1 4 2 2 6 6 7 1 6 6 5 5 5 7 6 6 5 7 6 7 6 5 4 7 2 7 7 6 5 7 4 7 3 1 5 2 4 6 6 6 4 6 4 5 7 1 7 6 6 4 6 6 7 5 7 5 6 7 6 1 6 5 6 4 6 5 7 4 7 6 6 5 7 7 1 2 1 1 1 1 1 1 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 1 1 1 2 2 2 1 1 2 2 1 3 4 3 1 3 2 3 4 4 3 2 3 2 1 2 2 3 2 2 3 2 2 2 2 4 3 4 3 2 3 3 3 4 2 4 2 3 4 4 4 1 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 U V W X Y Z AA 7 3 6 7 7 4 5 6 6 5 5 5 3 5 6 5 6 6 7 5 1 7 5 7 5 7 5 6 7 7 5 7 5 6 5 4 6 3 4 1 5 6 7 7 5 1 7 4 6 7 7 5 3 4 6 7 1 7 6 6 3 6 7 5 4 5 6 7 7 6 1 6 4 7 6 7 3 6 7 6 7 4 7 6 4 5 5 7 4 1 5 3 7 7 5 7 6 6 2 4 7 5 4 6 6 4 5 7 6 4 6 7 6 6 2 7 5 6 4 7 7 5 5 7 3 2 1 1 2 1 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 1 1 2 4 4 4 2 4 3 3 4 2 3 3 2 3 3 3 3 3 2 4 2 4 4 2 3 2 AB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 AC AD RESPMARI RESPHOUS RESPAGE 2 4 21 2 5 21 2 5 18 2 7 20 2 4 19 2 2 19 2 4 19 2 1 20 2 2 44 2 3 29 2 4 20 2 6 17 2 5 19 2 4 20 2 4 21 1 1 20 2 1 23 2 5 18 2 4 20 2 6 17 1 1 24 2 2 21 2 3 19 2 1 18 2 1 20 2 4 19 2 2 21 2 4 19 2 5 21 2 4 20 2 3 19 2 5 21 2 3 19 2 4 19 2 8 18 2 3 28 1 3 41 1 4 37 1 2 24 1 7 49 1 3 37 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 AB AC AD 1 2 1 1 1 1 2 1 1 2 2 1 2 2 1 2 1 2 2 1 2 2 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 2 2 1 1 2 1 6 3 3 4 1 4 6 1 5 1 7 5 5 6 5 4 3 6 7 7 1 1 3 6 1 2 5 6 2 7 6 1 4 7 2 7 2 5 3 3 24 22 40 46 32 36 70 21 46 40 66 49 80 38 32 68 64 18 35 66 20 52 27 46 30 25 36 28 64 38 69 44 28 69 55 45 27 66 38 45 61 38 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 AB AC AD 1 1 1 2 1 1 2 1 1 2 2 2 1 2 1 1 2 2 1 2 1 2 2 1 2 1 2 2 2 1 2 1 2 1 2 2 1 2 2 2 2 1 3 4 7 4 2 7 7 3 1 6 4 6 2 7 3 2 3 2 4 2 4 1 1 4 1 3 3 1 1 2 1 4 6 6 3 1 7 5 3 1 1 2 35 34 59 43 55 41 75 18 66 42 70 24 62 69 35 24 31 26 27 18 29 66 20 27 22 25 19 21 65 66 24 32 20 59 27 27 42 21 28 28 26 36 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 AB AC AD 2 1 2 1 1 1 1 1 2 2 2 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 2 1 5 4 5 2 4 4 1 4 5 4 4 1 6 2 2 1 3 7 3 6 3 6 53 61 25 31 50 35 70 22 25 21 23 39 33 37 18 33 21 65 22 31 53 36 57 33 44 Springdale Shopping Survey* The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey were as follows: A. How Often Respondent Shops at Each Area (Variables 1-3) 1. Springdale Mall 6 or more times/wk. 4-5 times/wk. 2-3 times/wk. 1 time/wk. 2-4 times/mo. 0-1 times/mo. 2. Downtown 3. West Mall (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) B. How Much the Respondent Spends during a Trip to Each Area (Variables 4-6) 4. Springdale Mall $200 or more $150-under $200 $100-under $150 $ 50-under $100 $ 25-under $50 $ 15-under $25 less than $15 5. Downtown 6. West Mall (1) (2) (3) (4) (5) (6) (7) (1) (2) (3) (4) (5) (6) (7) 8. Downtown 9. West Mall (5) (4) (3) (2) (1) (5) (4) (3) (2) (1) (1) (2) (3) (4) (5) (6) (7) C. General Attitude toward Each Shopping Area (Variables 7-9) 7. Springdale Mall Like very much Like Neutral Dislike Dislike very much (5) (4) (3) (2) (1) D. Which Shopping Area Best Fits Each Description (Variables 10-17) 10. 11. 12. 13. 14. 15. 16. 17. Easy to return/exchange goods High quality of goods Low prices Good variety of sizes/styles Sales staf helpful/friendly Convenient shopping hours Clean stores and surroundings A lot of bargain sales Springdale Mall Downtown West Mall No Opinion (1) (1) (1) (1) (1) (1) (1) (1) (2) (2) (2) (2) (2) (2) (2) (2) (3) (3) (3) (3) (3) (3) (3) (3) (4) (4) (4) (4) (4) (4) (4) (4) E. Importance of Each Item in Respondent's Choice of a Shopping Area (Variables 18-25) Not Important 18. 19. 20. 21. 22. 23. 24. 25. Easy to return/exchange goods High quality of goods Low prices Good variety of sizes/styles Sales staf helpful/friendly Convenient shopping hours Clean stores and surroundings A lot of bargain sales (1) (1) (1) (1) (1) (1) (1) (1) (2) (2) (2) (2) (2) (2) (2) (2) Very Important (3) (3) (3) (3) (3) (3) (3) (3) (4) (4) (4) (4) (4) (4) (4) (4) (5) (5) (5) (5) (5) (5) (5) (5) (6) (6) (6) (6) (6) (6) (6) (6) (7) (7) (7) (7) (7) (7) (7) (7) F. Information aboutt the Respondent (Variables 26-30) 26. Gender: (1) = Male (2) = Female 27. Number of years of school completed: (1) = less than 8 years (3) = 12-under 16 years (2) = 8-under 12 years (4) = 16 years or more 28. Marital status: (1) = Married (2) = Single or other 29. Number of people in household: persons 30. Age: years Each respondent in this database is described by 30 variables. As an example of their interpretation, consider row number 1. This corresponds to respondent number 1 and contains the following information. Variable number 6 = 7. The respondent usually spends less than $15 when she shops at West Mall. Variable number 26 = 2. The respondent is a female. 5556774441131111167765667232421 Variable number 1 = 5. The respondent shops at Springdale Mall 2-4 times/month. Variable number 19 = 7. Respondent believes \"high quality of goods\" is very important in choosing a shopping area. *Source: Materials for this case have been provided courtesy of The Archimedes Group, Indiana, PA. Data are based on actual responses obtained to this subset of the questions included in the survey; town and mall identities have been disguised as well as a number of responses were updated. The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file Shopping (attached below). The variables in the survey can be found in the file Coding (attached below). In this exercise, some of the estimation techniques presented in the module will be applied to the Springfield Shopping survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results. Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this module and applied here. 1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent's general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement. 1. Determine the point estimate, and then construct the 95% confidence interval for 7 = the average attitude toward Springdale Mall. 2. Repeat part (a) for 8 and 9, the average attitudes toward Downtown and West Mall, respectively. 2. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate and then construct the 95% confidence interval for p 26 = the population proportion of males. 3. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate and then construct the 95% confidence interval for p 28 = the population proportion in the \"single or other\" category. 4. Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each. If the managers want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample size be for each mall? 1.The point estimate and the 95% confidence interval for 7 = the average attitude toward Springdale Mall is The point estimate x x n standard deviation x x SD 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.813 Standard deviation 1.064 Standard error 0.087 t-significant value at 5% 1.976 Point estimate 3.813 95% Lower limit 3.642 95% upper limit 3.985 2. The point estimate and the 95% confidence interval for 8 = the average attitude toward Down town Mall is The point estimate x x n standard deviation x x SD 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.407 Standard deviation 1.124 Standard error 0.092 t-significant value at 5% 1.976 Point estimate 3.407 95% Lower limit 3.225 95% upperlimit 3.588 3. The point estimate and the 95% confidence interval for 9 = the average attitude toward West Mall is The point estimate x x n standard deviation SD x x 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.287 Standard deviation 1.183 Standard error 0.097 t-significant value at 5% 1.976 Point estimate 3.287 95% Lower limit 3.096 95% upper limit 3.478 II The point estimate and the 95% confidence interval for p 26 = the population proportion of males is Point estimate p No.of Males n 95% confidence interval for population proportion of males is p Z 0.05/2 p 1 p n Count 150 No.of Males 64 No.of Females 86 Proportion of Males 0.427 Z value at 0.05/2 level 1.960 Standard error 0.040 Point estimate 0.427 95% confidence interval lower limit 0.348 95% confidence interval upper limit 0.506 III The point estimate and the 95% confidence interval for p 28 = the population proportion in the \"single or other\" category is Point estimate p No.of single or other n 95% confidence interval for population proportion single or other is p Z 0.05/2 Count 150 p1 p n NO. of Single or other 83 No.of Married 67 Proportion of single or other 0.553 Z value at 0.05/2 level 1.960 Standard error 0.041 Point estimate 0.553 95% confidence interval lower limit 0.474 95% confidence interval upper limit 0.633 IV. The estimated sample sizes for each of the sample with the margin of error 0.05 with 95% confidence is 2 * SD Z Sample size 0.05/2 ME SPRINGDALE DOWN TOWN Margin of error WEST 0.05 0.05 0.05 1.064 1.124 1.183 Z-value at 0.05/2 level 1.96 1.96 1.96 Sample size 1741 1941 2152 Standard deviation The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file Shopping (attached below). The variables in the survey can be found in the file Coding (attached below). In this exercise, some of the estimation techniques presented in the module will be applied to the Springfield Shopping survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community, and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results. Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this module and applied here. 1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent's general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement. 1. Determine the point estimate, and then construct the 95% confidence interval for 7 = the average attitude toward Springdale Mall. 2. Repeat part (a) for 8 and 9, the average attitudes toward Downtown and West Mall, respectively. 2. Given the breakdown of responses for variable 26 (sex of respondent), determine the point estimate and then construct the 95% confidence interval for p 26 = the population proportion of males. 3. Given the breakdown of responses for variable 28 (marital status of respondent), determine the point estimate and then construct the 95% confidence interval for p 28 = the population proportion in the \"single or other\" category. 4. Assume the managers have requested estimates of the mean attitudes towards each mall with a margin of error of 0.05 for each. If the managers want to have 95% confidence that the sample mean will fall within this margin of error, how large should the sample size be for each mall? 1.The point estimate and the 95% confidence interval for 7 = the average attitude toward Springdale Mall is The point estimate x x n standard deviation x x SD 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.813 Standard deviation 1.064 Standard error 0.087 t-significant value at 5% 1.976 Point estimate 3.813 95% Lower limit 3.642 95% upper limit 3.985 2. The point estimate and the 95% confidence interval for 8 = the average attitude toward Down town Mall is The point estimate x x n standard deviation x x SD 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.407 Standard deviation 1.124 Standard error 0.092 t-significant value at 5% 1.976 Point estimate 3.407 95% Lower limit 3.225 95% upperlimit 3.588 3. The point estimate and the 95% confidence interval for 9 = the average attitude toward West Mall is The point estimate x x n standard deviation SD x x 2 n 1 The 95% confidence interval for mean average attitude is x t0.05/2, n 1 Count SD n 150 Average 3.287 Standard deviation 1.183 Standard error 0.097 t-significant value at 5% 1.976 Point estimate 3.287 95% Lower limit 3.096 95% upper limit 3.478 II The point estimate and the 95% confidence interval for p 26 = the population proportion of males is Point estimate p No.of Males n 95% confidence interval for population proportion of males is p Z 0.05/2 p 1 p n Count 150 No.of Males 64 No.of Females 86 Proportion of Males 0.427 Z value at 0.05/2 level 1.960 Standard error 0.040 Point estimate 0.427 95% confidence interval lower limit 0.348 95% confidence interval upper limit 0.506 III The point estimate and the 95% confidence interval for p 28 = the population proportion in the \"single or other\" category is Point estimate p No.of single or other n 95% confidence interval for population proportion single or other is p Z 0.05/2 Count 150 p1 p n NO. of Single or other 83 No.of Married 67 Proportion of single or other 0.553 Z value at 0.05/2 level 1.960 Standard error 0.041 Point estimate 0.553 95% confidence interval lower limit 0.474 95% confidence interval upper limit 0.633 IV. The estimated sample sizes for each of the sample with the margin of error 0.05 with 95% confidence is 2 * SD Z Sample size 0.05/2 ME SPRINGDALE DOWN TOWN Margin of error WEST 0.05 0.05 0.05 1.064 1.124 1.183 Z-value at 0.05/2 level 1.96 1.96 1.96 Sample size 1741 1941 2152 Standard deviation