Homework SourseThere are 7 parts to this assignment Please label them in yo
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.)
Solution
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 |
