Question
The Importance of Random Selection Background This exercise will demonstrate that random selection is important for obtaining a representative sample of the population in order
The Importance of Random Selection
Background
This exercise will demonstrate that random selection is important for obtaining a representative sample of the population in order to avoid bias. Bias is when we consistently overestimate or underestimate a population parameter.
In statistics, we often want to extend results beyond the particular group studied to a larger group, the population. We are trying to gain information about the population by examining a portion of the population, called a sample. Such generalizations are only valid if the data (sample) are representative of that larger group (population). A representative sample is one in which the relevant characteristics of the sample members are generally the same as those of the population. Improper or biased sample selection tends to systematically favor certain outcomes and can produce misleading results and erroneous conclusions.
Suppose a park is being tested for an infestation of aphids, which can impact the radial growth (diameter) of the trees. The tree map represent the diameters of a population of 80 tree trunks in a park. There are only 3 sizes of tree trunks: small, medium, and large. A sample of tree diameters needs to be measured to see if the average diameter of the trees in the park is similar to other parks. Two sampling methods will be utilized: Judgement sample, and Simple Random sample. The resulting estimates of mean (average) diameters will be compared to the population diameter to see which sample was a better estimate.
Below is a map of the trees numbered 1-80. When selecting the trees, the numbers on the map are the identifier of the trees and the diameter can be estimated by the size of the circle. For example, Tree number 16 is a small, 8 is a medium, and 17 is a large. They have diameters of 1, 2, and 3 respectively.
Tree diameters population
| Tree Number | Diameter | Size |
| 1 | 2 | M |
| 2 | 1 | S |
| 3 | 2 | M |
| 4 | 1 | S |
| 5 | 1 | S |
| 6 | 1 | S |
| 7 | 1 | S |
| 8 | 2 | M |
| 9 | 1 | S |
| 10 | 1 | S |
| 11 | 1 | S |
| 12 | 1 | S |
| 13 | 1 | S |
| 14 | 2 | M |
| 15 | 1 | S |
| 16 | 1 | S |
| 17 | 3 | L |
| 18 | 1 | S |
| 19 | 1 | S |
| 20 | 2 | M |
| 21 | 1 | S |
| 22 | 1 | S |
| 23 | 1 | S |
| 24 | 1 | S |
| 25 | 1 | S |
| 26 | 1 | S |
| 27 | 1 | S |
| 28 | 1 | S |
| 29 | 2 | M |
| 30 | 1 | S |
| 31 | 1 | S |
| 32 | 2 | M |
| 33 | 1 | S |
| 34 | 1 | S |
| 35 | 1 | S |
| 36 | 3 | L |
| 37 | 1 | S |
| 38 | 2 | M |
| 39 | 1 | S |
| 40 | 2 | M |
| 41 | 1 | S |
| 42 | 1 | S |
| 43 | 1 | S |
| 44 | 1 | S |
| 45 | 1 | S |
| 46 | 1 | S |
| 47 | 1 | S |
| 48 | 1 | S |
| 49 | 2 | M |
| 50 | 1 | S |
| 51 | 1 | S |
| 52 | 2 | M |
| 53 | 1 | S |
| 54 | 2 | M |
| 55 | 2 | M |
| 56 | 1 | S |
| 57 | 1 | S |
| 58 | 1 | S |
| 59 | 1 | S |
| 60 | 1 | S |
| 61 | 1 | S |
| 62 | 1 | S |
| 63 | 1 | S |
| 64 | 2 | M |
| 65 | 1 | S |
| 66 | 1 | S |
| 67 | 1 | S |
| 68 | 3 | L |
| 69 | 1 | S |
| 70 | 1 | S |
| 71 | 1 | S |
| 72 | 1 | S |
| 73 | 1 | S |
| 74 | 1 | S |
| 75 | 1 | S |
| 76 | 1 | S |
| 77 | 1 | S |
| 78 | 1 | S |
| 79 | 1 | S |
| 80 | 1 | S |
Random selection lab tree map numbered
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Entrepreneurship
Authors: Andrew Zacharakis, William D Bygrave
5th Edition
1119563097, 9781119563099
