A. Download the data set for this assignment.

Let's assume this data set is our population (all MATH classes who have taken this survey about how far you live from your school) with N=1,800. First, we need to examine the variable "Miles". This variable is the number of miles a student is from home. Use Stats/Basic Statistics/Display Descriptive Statistics to find the mean and standard deviation of this population. This will be (population mean) and (population standard deviation) respectively. Normally, we don't know and . But we do in this case for illustration purposes.

1. What is the mean () and the standard deviation () for this population?
2. We will now take a random sample of size n=200 from our population. To do this, open Calc>Sample from Cloumns. For the "Number of rows to sample" input 200. "From Columns" select the (Miles). "Store samples in" any new column. Don't click on the sample with replacement box.
3. Using the sample you created in 2, construct and write a 95% Confidence Interval for . Does your Confidence Interval include ? Interpret the confidence interval. (Remember to explain if CLT is met or not).
4. How large a sample is required to estimate the mean of the variable "Miles" within 50 miles (error) with 95% confidence? (Use the population standard deviation).

B. The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The data represent the diameter in centimeters of a random sample of 12 Douglas firs in the western Washington Cascades.

1. Obtain a point estimate for the mean and standard deviation diameter of a Douglas fir tree in the western Washington Cascades.
2. Construct a 95% confidence interval for the mean diameter of a Douglas fir tree in the western Washington Cascades.

156	162
190	130
147	101
173	147
159	113
181	109

Data

Miles. 130 150 150 500 130 137 30 120 120 150 150 140 65 122.8 100 18 40 150 110 160 60 150 6 400 200 45.6 7 20 70 115 0 150 55 100 160 150 20 140 130 155 120 30 200 60 70 150 100 100 120 40 147 20 180 110 15 32 150 5 130 20 125.49 120 43 55 300 75 130 80 123.75 170 45 130 145 38 200 267 120 750 17 20 35 150 21 15 60 365 65.79 100 90 69 130 360 100 70 150 100 20 75 105 140 50 160 86 40 126 135 140 100 50 150 86 145 130 150 65 200 150 90 74 142 130 150 200 135 165 460 55 150 97 20 375 130 0 130 141 15 160 60 70 350 100 150 140 190 1 80 80 300 70 110 5 78 100 0.8 60 650 35 185 150 414 30 35 140 90 30 200 200 360 150 100 90 140 220 91 150 180 40 1 120 150 135 93 120 2 170 75 75 45 150 300 150 95 132 321 70 70 216 130 140 110 105 100 110 120 110 100 150 180 17 85 180 148 146 45 95 160 90 128 8 148 100 180 150 4 150 140 50 50 85 150 91 99.99 80 120 130 47 106 120 100 93 160 200 302 1.5 230 90 30 180 120 30 140 100 40 20 200 120 100 1 40 90 125 70 110 146 100 120 45 75 50 45 160 161 200 185 80 35 150 80 100 85 30 68 10 66.37 110 50 120 140 12 20 140 7 65 75 160 150 150 145 115 150 120 124 200 150 152 100 144 45 100 685 75 144 65 200 150 84 0 140 148 128 90 100 136 2 20 110 113 190 120 108 20 90 10 63 110 145 225 95 65 120 115 350 45 330 5 60 130 165 130 70 45 45 160 100 153 150 112 160 154 100 120 160 120 20 45 130 110 150 100 64 1 200 147 42 150 168 154 141 110 115 80 120 135 78 51 360 48 100 170 130 176 5 1000 40 200 125 60 150 0 0 531 130 5 238 98 90 250 150 130 380 15 285 3 120 144 110 110 80 65 130 42.3 12 8 100 145 150 110 150 110 43 40 48 30 95 250 130 0 124 115 1 60 160 120 135 68 105 30 130 104 150 46 2 200 144 18 215 450 140 145 70 70 150 113 120 140 135 100 100 0 90 1 160 100 65 90 160 150 140 110 200 15 60 102 100 6 100 150 130 140 200 167 80 3 120 93 3 60 90 155.87 150 142 120 110 144 1000 160 110 162 3 120 200 43.07 60 200 200 20 110 152 150 5 120 140 200 80 150 140 50 85 80 126 220 45 80 500 1 158 30 250 120 13 82 75 155 120 100 200 140 1.5 65 85 140 80 85 60 120 160 5 196 150 130 110 120 501 100 45 120 110 60 85 55 122 90 15 140 165 65 60 120 100 148 150 80 63 50 98 10 60 153 150 153 10 2 72 170 150 12 90 200 126 115 90 35 32 40 400 140 50 136 100 72 90 2 55 110 35 1500 125 1500 160 8 135 120 143.67 200 110 249 20 136 58 1 1 80 95 35 60 70 315 90 100 113 65 65 141 39.8 80 15 75.6 75 95 150 160 55 90 158 120 15 25 300 160 170 125 142 80 3 75 200 120 130 5 110 150 40 143 50 279 150 13 170 175 140 100 175 22 5 100 300 120 40 170 150 150 165 156 50 141 80 115 130 50 1 140 150 97 100 100 144 65 75 170 6 360 1000 52 200 200 20 255 98 100 100 200 60 130 250 90 5 700 7 130 120 150 75 225 110 910 131 90 150 75 100 15 2 2 140 120 133 180 60 150 60 75 50 240 180 160 354 357 25 120 636.58 100 80 2.5 60 80 200 100 150 140 86.8 15 0 45 30 871 25 76 110 160 180 2 150 69 120 200 120 84 25 100 15 150 80 140 70 3 43 110 230 150 110 110 150 125 135 15 212 974 125 20 150 75 230 175 160 220 180 100 114.79 25 70 145 75 1687 130 65 120 58 130 155 121 70 62 60 160 20 15 43 125 65 140 145 115 92 50 95 150 56 120 100 120 75 85 135 150 120 8 75 4 1234 100 0 50 40 150 95 100 147.5 145 180 100 62 110 20 150 109.1 200 5 1 30 250 110 0 220 75 145 75 86.5 140 150 5 40 120 0 120 10 150 135 0 120 220 110 115 120 100 130 50 115 30 110 5 0 155 130 173 120 75 100 31.01 200 8 77 143 90 165 75 172 200 1 160 40 60 150 134 70 175 300 160 100 55 52 167 139 150 120 150 150 165 15 179 115 136 110 150 180 160 70 120 80 100 157.54 20 150 212 5 157 2 215 140 7 90 20 35 135 200 128 150 300 144 73 55 160 100 85 0 100 130 150 90 154 22 140 70 98 95 200 104 130 1 40 250 160 636.58 150 160 85 96 133 60 45 100 35 35 90 141 200 160 150 238 58 600 64 130 28 160 90 120 550 170 157 162 62 104 7 30 120 65 174 175 200 350 30 115 180 20 90 160 25 60 150 176 184 80 95 150 45 129 80 325 150 15 150 61 80 141 158 120 20 112 101.3 81 200 150 50 100 2100 45 165 115 125 200 80 102 160 175 140 110 7 60 825 180 145 124 150 140 115 45 120 45 140 15 54 140 75 105 63.77 3 135 15 258 130 125 90 250 110 30 50 168 150 140 140 160 115 120 210 135 225 150 152 150 30 302 55 155 120 1500 129 350 5 130 120 20 145 370 50 160 200 144 35 165 200 148 125 130 100 75 35 150 145 95 95 180 45 45 20 25 200 42 150 100 55 160 65 32 150 150 15 110 101 10 800 144 40 150 120 90 160 100 60 12 74 90 0 125 85 130 367 75 140 130 120 100 256 60 115 30 500 90 110 1 130 200 175 155 150 125 157.43 135 170 60 3 130 40 80 70 180 5 165 110 175 120 55 40 150 150 680 100 160 50 40 100 95 50 61 32 160 111 50 62 100 150 132 150 140 70 140 110 340 150 150 126 50 40 150 375 15 65 90 90 60 200 50 120 140 85 0 85 65 173 5 155 144 60 133 69 110 200 150 28 100 150 160 90 130 375 100 181 200 10 2 150 130 60 250 130 90 45 65 200 154.04 152 80 134 275 60 1 170 100 50 145.2 10 500 150 120 150 126.8 100 153 410 0 60 95 150 70 130 12 150 153 113 160 235 180 200 71 80 150 30 60 80 54 30 170 100 314 145 1000 130 75 53 130 130 110 45 80 3 152 42 85 250 60 111 110 80 200 10 120 95 85 1 145 73 50 132 137 150 45 160 70 161 15 110 1 200 123 150 130 420 140 60 200 100 155 200 8 125 150 1500 120 100 150 70 150 160 120 110 70 130 794 95 30 425 30 100 140 120 157 115 732 80 5 142 120 8 145 120 120 143 72 15 130 30 150 100 25 180 40 8 110 140 60 25 100 150 89 72 60 350 150 45 140 1200 120 60 150 142 153 150 150 80 75 75 253 450 100 200 25 150 70 50 50 160 130 37 15 140 40 120 70 70 75 115 5 25 125 75 80 190 140 100 360 140 110 45 175 30 170 130 120 7.8 328 250 5 300 320 163 8 19 150 300 100 20 87 72 43 70 150 170 90 40 120 90 150 90 115 130 102 150 800 54 497 150 80 65 60 139 120 130 150 140 260 160 100 65 350 155 43 115 10 20 75 152 100 167 120 76 70 150 177 120 20 40 100 75 130 973 30 150 40 88 120 65 100 151.12 170 100 126 250 50 120 130 60 100 10 98 200 104 67.76 75 117 150 110 30 15 168 25 155.26 120 20 144.77 35 120 225 30 8 65 150 160 100 145 5 110 100 230 38 144 45 145 140 321 90 15 45 180 130 50 55 100 98 110 2 130 98 27 125 157 70 40 200 120 140 125 70 150 75 50 30 90 60 120 130 100 140 4 130 75 130 95 150 178 80 175 94.6 100 200 200 2 27 120 1000 2 45 144 145 90 130 26 80 54 200 120 135 120 160 120 146 130 144 77 20 54 97 200 84 100 142 135 95 150 250 70 71.39 450 30 118 160 160 94 0 130 165 150 40 120 35 1500 7 0 100 165 144 160 125 85 160 100 80 160 100 110 39.8 15 1768 125 121 70 100 115 160 120 250 142 90 20 12 996 55 40 160 100 0 250 150 60 200 150 120 185 140 200 77 90 125 90 70 30 100 275 150 148 300 10 100 50 30 200 2 95 51.5 97 160 72 85 307 5 130 85 60 60 30 23 120