Question

in rocky mountain national park, many mature pine trees along highway 34 are dying due to infestation by pine beetles. scientists would like to use a sample of size 200 to estimate the proportion of the approximately 5000 pine trees along the highway that have been infested. describe how to select a systematic random sample of 200 pine trees along highway 34. because there are 5,000 pine trees that are along highway 34 and our desired sample size is 200, we would like to select every 25th pine tree . for simplicity, we could walk down highway 34 and select every 25th pine tree that we pass . to choose a starting point, we randomly select a number from 1 to 5000 . we would select that pine tree and every 25th pine tree thereafter until 200 pine trees have been selected.

Answer 1

To perform a systematic random sample of pine trees, select every 25th tree after choosing a random starting point between 1 and 25, until 200 trees are sampled.

Step-by-step explanation:

To select a systematic random sample of 200 pine trees along highway 34 in Rocky Mountain National Park for estimating the proportion of trees infested by pine beetles, you would first need to create a sampling frame of the 5000 pine trees. Since the desired sample size is 200, you would select every 25th tree to achieve this; this is known as the sampling interval, calculated by dividing the population size by the sample size (5000/200). You would begin by choosing a random starting point between 1 and 25. This random number will be the first tree you sample. You would then proceed to select every 25th pine tree from this starting point (for example, if you start at tree number 6, the subsequent trees you select would be numbers 31, 56, 81, and so on), continuing this process until you have selected 200 trees.

Answer 2

To estimate the proportion of pine trees infested by pine beetles, scientists can use a systematic random sampling method by selecting every 25th pine tree after determining a random starting point between 1 and 25. This process is repeated until a sample of 200 is achieved, ensuring a fair representation of the 5000 trees along highway 34.

Step-by-step explanation:

To select a systematic random sample of 200 pine trees in Rocky Mountain National Park along highway 34, scientists could implement the following procedure:

• Start by determining the interval at which to select the trees. Since there are about 5000 pine trees and we want a sample size of 200, we would select every 25th pine tree (5000 ÷ 200 = 25).
• To avoid bias, randomly choose a starting point between 1 and 25. This can be done using random number generation tools or simply drawing a number from a hat.
• The selected starting point will be the first tree in your sample.
• From there, continue to select every 25th tree. If you start with tree number 10, the next trees would be number 35, 60, 85, and so on.
• Continue this process until you have selected 200 trees. If the end of the area is reached before 200 trees have been sampled, continue counting from the beginning.

This method ensures that every tree has an equal chance of being selected, and the systematic approach ensures a spread of sampling throughout the approximate 5000 trees along the highway.