Forest rangers at a national park want to take a sample of trees to estimate what proportion of trees in the park are infected with a certain disease. The population of trees in question is divided by a creek. East of the creek, most of the trees are oak. West of the creek, most trees are cedar, which are more likely to be infected. The rangers are considering taking a stratified random sample using each side of the creek as strata. They'll sample trees from each side proportionately based on the total number of trees on each side. Why might the rangers choose stratification instead of a simple random sample to estimate the proportion of infected trees?

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Answer:

In the use of repeated sampling,  the estimates from this sort of stratified sample would likely vary less than estimates from simple random samples. the use of stratified random sample is important because it  reduces the likelihood of getting disproportionate numbers of cedar or oak trees in the sample.

Step-by-step explanation:

TL; DR Its because stratification is related to subdivision(strata) in the population based on categories, whereas the simple random sampling selects individuals randomly, without any consideration of subdivisions.

Given Data:

Forest rangers want to sample forest.

National park is sampled to estimate a category named as "trees infected with certain disease"

East creek has oak trees ( a category or division)

West has Cedar trees, more likely to be affected.

Such types of sub division based on categories tells that the population(here trees in the national park) are weighted in some parks (like cedar tree group in west of the creek).

We do SRS (Simple random Sampling) when the whole population is not being looked as made up of partitions. It is seen as a whole and not divided into categories which can weightily affect the  estimation process more than other part of the same population for sure.

Stratified sampling on the other hand is based for the same purpose of doing sampling from the population which is seen to be composed of categories (like in this case where national park trees are group of composed of oak trees which are less probable to disease and the cedar trees in west which are more probable to get infected).

The smaller groups used in stratification are called strata.

That's why we will use Stratified sampling or the process of stratification instead of a simple random sample to estimate the proportion of infected trees.

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