There are 7 parts to this assignment. Please label them in your WORD DOC report
ID: 3394068 • Letter: T
Question
There are 7 parts to this assignment. Please label them in your WORD DOC report (NOT EXCEL file) to me as Part 1, Part 2, etc.
As before send them to my Graduate Assistant.
Part 1:
Using Excel’s Randbetween(0,9) function, generate 200 samples of five random numbers between 0 and 9, calculate the mean of each sample. Show me the list of the 200 means. Typically, they should look like: 4.8, 3.6, 4.4, 6.0, etc.
Part 2:
Using Excel, calculate the overall mean of the 200 sample means (the average of the averages). This should be around 4.5.
Part 3:
Using Excel, calculate the standard error of the mean (SEM) (i.e. the standard deviation of the 200 sample means). We established in the previous simulation that the population average is 4.5 and the standard deviation of the population is 2.87.
Since the SEM= = /n. and n=5, the SEM therefore is 1.28. Thus, the standard deviation of the 200 sample means should be approximately 1.28.
Part 4:
Using Excel, make the histogram of the 200 sample means (sampling distribution of the mean) (use interval size 1, i.e., 0-1, 1-2, 2-3, …8-9). According to the Central Limit Theorem a bell shaped curve should appear. Show me this graph.
Part 5:
Discuss the intuitive logic of the Central Limit Theorem. Discuss the implications of part 4 in this context. (My videos might help here.)
Part 6:
Use 2 methods to find P (>6.3), (with n=5 as in Parts 1-4): First the z-method of chapter 7 and then by simply counting how many of your 200 were above 6.3.
Part 7:
Discuss the standard error of the mean. (Explain clearly the reasons why there is an “n” in the bottom of the formula; my video might help here as well.)
Explanation / Answer
Part-1
using Randbetween(0,9) this code in excel , we gnerate 200 sample of sample size 5 and calculte the sample mean recorded in Table.
Part-2
Using Avrage() code we calculate the sample mean of the each sample and the overall mean also calculated and we find that overall mean is arround 4.5.as shown in Table
part-3
STDEV using this code we calculate the sample std. deviation for each sample and sample error mean also in Table.
Table
1.222
Sample R1 R2 R3 R4 R5 Sample mean standard deviation SEM 1 8 7 1 0 3 3.8 3.564 1.594 2 9 2 2 0 6 3.8 3.633 1.625 3 4 3 6 9 0 4.4 3.362 1.503 4 7 3 5 2 8 5 2.550 1.140 5 4 6 1 5 2 3.6 2.074 0.927 6 2 8 7 5 9 6.2 2.775 1.241 7 9 3 8 2 9 6.2 3.421 1.530 8 8 1 4 8 9 6 3.391 1.517 9 5 9 8 0 0 4.4 4.278 1.913 10 3 8 4 1 5 4.2 2.588 1.158 11 1 0 1 5 5 2.4 2.408 1.077 12 1 9 9 7 1 5.4 4.099 1.833 13 8 1 7 6 1 4.6 3.362 1.503 14 0 8 6 0 0 2.8 3.899 1.744 15 3 3 9 6 1 4.4 3.130 1.400 16 1 2 8 8 8 5.4 3.578 1.600 17 8 7 3 3 9 6 2.828 1.265 18 5 3 2 0 6 3.2 2.387 1.068 19 5 8 0 0 5 3.6 3.507 1.568 20 4 3 2 5 8 4.4 2.302 1.030 21 4 5 7 0 1 3.4 2.881 1.288 22 2 7 6 4 9 5.6 2.702 1.208 23 6 0 5 1 8 4 3.391 1.517 24 8 3 5 3 7 5.2 2.280 1.020 25 2 1 1 2 4 2 1.225 0.548 26 5 7 1 7 3 4.6 2.608 1.166 27 8 5 8 7 3 6.2 2.168 0.970 28 7 2 7 3 4 4.6 2.302 1.030 29 3 3 8 2 5 4.2 2.387 1.068 30 8 7 6 2 1 4.8 3.114 1.393 31 6 9 0 5 9 5.8 3.701 1.655 32 4 5 8 8 3 5.6 2.302 1.030 33 2 2 9 6 3 4.4 3.050 1.364 34 8 5 2 3 6 4.8 2.387 1.068 35 6 2 7 7 5 5.4 2.074 0.927 36 4 9 7 1 9 6 3.464 1.549 37 2 6 1 3 3 3 1.871 0.837 38 9 3 1 2 3 3.6 3.130 1.400 39 6 8 5 2 0 4.2 3.194 1.428 40 8 7 2 2 9 5.6 3.362 1.503 41 1 5 7 8 1 4.4 3.286 1.470 42 8 7 4 7 9 7 1.871 0.837 43 0 3 1 6 2 2.4 2.302 1.030 44 7 3 9 4 2 5 2.915 1.304 45 4 9 7 2 1 4.6 3.362 1.503 46 5 8 4 0 6 4.6 2.966 1.327 47 6 9 6 0 3 4.8 3.421 1.530 48 4 7 1 3 4 3.8 2.168 0.970 49 4 6 5 9 5 5.8 1.924 0.860 50 8 1 1 5 9 4.8 3.768 1.685 51 3 3 7 4 3 4 1.732 0.775 52 9 9 7 9 4 7.6 2.191 0.980 53 8 9 4 6 7 6.8 1.924 0.860 54 7 0 0 6 2 3 3.317 1.483 55 1 1 6 1 2 2.2 2.168 0.970 56 5 4 0 3 6 3.6 2.302 1.030 57 4 7 5 9 0 5 3.391 1.517 58 8 3 2 2 1 3.2 2.775 1.241 59 6 2 9 6 4 5.4 2.608 1.166 60 9 4 7 8 1 5.8 3.271 1.463 61 7 6 6 3 5 5.4 1.517 0.678 62 2 4 9 2 6 4.6 2.966 1.327 63 6 5 0 1 3 3 2.550 1.140 64 6 5 5 1 4 4.2 1.924 0.860 65 6 6 3 9 6 6 2.121 0.949 66 5 5 6 4 3 4.6 1.140 0.510 67 9 7 9 4 5 6.8 2.280 1.020 68 1 2 0 9 2 2.8 3.564 1.594 69 7 3 7 6 8 6.2 1.924 0.860 70 5 9 9 7 8 7.6 1.673 0.748 71 2 6 3 4 3 3.6 1.517 0.678 72 1 2 2 8 2 3 2.828 1.265 73 9 4 0 3 1 3.4 3.507 1.568 74 4 3 0 5 7 3.8 2.588 1.158 75 8 0 8 4 7 5.4 3.435 1.536 76 8 6 9 4 8 7 2.000 0.894 77 5 3 9 3 7 5.4 2.608 1.166 78 5 1 9 6 4 5 2.915 1.304 79 4 6 3 4 4 4.2 1.095 0.490 80 5 9 0 2 7 4.6 3.647 1.631 81 8 0 4 6 9 5.4 3.578 1.600 82 3 5 5 3 0 3.2 2.049 0.917 83 4 8 6 5 2 5 2.236 1.000 84 8 9 4 8 0 5.8 3.768 1.685 85 1 9 2 2 0 2.8 3.564 1.594 86 1 3 1 5 4 2.8 1.789 0.800 87 8 3 4 7 7 5.8 2.168 0.970 88 8 1 2 4 5 4 2.739 1.225 89 7 6 9 2 5 5.8 2.588 1.158 90 5 1 2 5 8 4.2 2.775 1.241 91 8 1 4 3 2 3.6 2.702 1.208 92 9 9 1 5 8 6.4 3.435 1.536 93 5 8 7 9 1 6 3.162 1.414 94 3 3 2 9 2 3.8 2.950 1.319 95 1 9 6 8 1 5 3.808 1.703 96 4 7 5 2 3 4.2 1.924 0.860 97 7 8 1 4 2 4.4 3.050 1.364 98 9 6 3 6 4 5.6 2.302 1.030 99 9 4 3 6 6 5.6 2.302 1.030 100 8 4 6 6 7 6.2 1.483 0.663 101 0 0 3 5 3 2.2 2.168 0.970 102 2 0 2 0 9 2.6 3.715 1.661 103 7 0 8 0 0 3 4.123 1.844 104 6 5 2 7 5 5 1.871 0.837 105 7 4 4 7 9 6.2 2.168 0.970 106 1 6 8 3 1 3.8 3.114 1.393 107 4 8 3 6 6 5.4 1.949 0.872 108 4 8 0 7 5 4.8 3.114 1.393 109 8 9 8 8 0 6.6 3.715 1.661 110 8 0 8 5 5 5.2 3.271 1.463 111 6 3 0 3 7 3.8 2.775 1.241 112 3 2 8 5 7 5 2.550 1.140 113 3 8 0 4 0 3 3.317 1.483 114 2 8 8 8 9 7 2.828 1.265 115 4 6 7 2 0 3.8 2.864 1.281 116 3 5 3 1 8 4 2.646 1.183 117 8 2 2 3 4 3.8 2.490 1.114 118 4 8 1 3 2 3.6 2.702 1.208 119 7 8 4 9 7 7 1.871 0.837 120 3 2 1 7 2 3 2.345 1.049 121 6 6 6 1 5 4.8 2.168 0.970 122 5 0 9 7 4 5 3.391 1.517 123 8 0 8 4 8 5.6 3.578 1.600 124 6 8 8 9 5 7.2 1.643 0.735 125 4 6 3 3 1 3.4 1.817 0.812 126 7 3 6 7 0 4.6 3.050 1.364 127 6 9 8 3 9 7 2.550 1.140 128 7 6 1 4 9 5.4 3.050 1.364 129 7 0 3 7 6 4.6 3.050 1.364 130 6 9 5 5 3 5.6 2.191 0.980 131 4 4 3 9 8 5.6 2.702 1.208 132 8 3 2 8 3 4.8 2.950 1.319 133 0 3 4 3 0 2 1.871 0.837 134 5 1 0 7 9 4.4 3.847 1.720 135 5 4 3 9 9 6 2.828 1.265 136 4 2 4 6 7 4.6 1.949 0.872 137 4 5 3 0 9 4.2 3.271 1.463 138 5 0 0 1 3 1.8 2.168 0.970 139 7 1 1 1 1 2.2 2.683 1.200 140 8 9 8 9 1 7 3.391 1.517 141 8 3 0 1 0 2.4 3.362 1.503 142 4 7 7 5 5 5.6 1.342 0.600 143 8 3 6 6 4 5.4 1.949 0.872 144 1 9 1 9 2 4.4 4.219 1.887 145 5 2 9 1 2 3.8 3.271 1.463 146 1 3 8 5 8 5 3.082 1.378 147 8 1 6 1 4 4 3.082 1.378 148 6 0 9 9 4 5.6 3.782 1.691 149 8 7 9 0 2 5.2 3.962 1.772 150 5 3 0 6 5 3.8 2.387 1.068 151 6 9 4 9 9 7.4 2.302 1.030 152 3 2 2 1 5 2.6 1.517 0.678 153 9 1 1 0 2 2.6 3.647 1.631 154 9 0 9 7 0 5 4.637 2.074 155 4 1 4 5 3 3.4 1.517 0.678 156 5 3 0 0 8 3.2 3.421 1.530 157 1 0 0 4 4 1.8 2.049 0.917 158 6 1 5 9 2 4.6 3.209 1.435 159 0 4 9 4 7 4.8 3.421 1.530 160 4 5 5 6 6 5.2 0.837 0.374 161 8 8 8 3 2 5.8 3.033 1.356 162 3 7 9 0 0 3.8 4.087 1.828 163 1 1 5 7 9 4.6 3.578 1.600 164 0 7 6 0 5 3.6 3.362 1.503 165 8 2 4 3 6 4.6 2.408 1.077 166 0 5 9 4 1 3.8 3.564 1.594 167 6 1 0 3 1 2.2 2.387 1.068 168 5 5 4 2 6 4.4 1.517 0.678 169 6 1 5 7 6 5 2.345 1.049 170 8 8 3 3 1 4.6 3.209 1.435 171 6 4 5 8 3 5.2 1.924 0.860 172 1 0 8 3 5 3.4 3.209 1.435 173 4 5 1 7 2 3.8 2.387 1.068 174 8 5 5 5 0 4.6 2.881 1.288 175 9 9 3 9 3 6.6 3.286 1.470 176 5 6 5 7 1 4.8 2.280 1.020 177 3 4 7 1 9 4.8 3.194 1.428 178 8 3 8 4 3 5.2 2.588 1.158 179 3 1 5 5 7 4.2 2.280 1.020 180 8 6 5 3 9 6.2 2.387 1.068 181 8 0 4 1 3 3.2 3.114 1.393 182 3 6 6 8 8 6.2 2.049 0.917 183 5 1 1 9 9 5 4.000 1.789 184 3 6 6 2 7 4.8 2.168 0.970 185 0 7 8 6 4 5 3.162 1.414 186 3 2 4 6 5 4 1.581 0.707 187 4 6 3 6 6 5 1.414 0.632 188 8 6 8 0 3 5 3.464 1.549 189 7 5 5 7 0 4.8 2.864 1.281 190 9 4 3 8 6 6 2.550 1.140 191 3 6 3 8 2 4.4 2.510 1.122 192 2 5 0 0 6 2.6 2.793 1.249 193 6 4 1 8 9 5.6 3.209 1.435 194 1 8 6 3 2 4 2.915 1.304 195 6 9 4 2 7 5.6 2.702 1.208 196 7 6 8 9 2 6.4 2.702 1.208 197 5 3 6 6 6 5.2 1.304 0.583 198 3 7 8 8 5 6.2 2.168 0.970 199 4 4 2 6 8 4.8 2.280 1.020 200 5 3 7 2 2 3.8 2.168 0.970 Overall mean 4.64 200 sample mean standard deviation 2.732 standard error of the mean (SEM)1.222
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