Question

Suppose you have two​ populations: Population Along dashAll students at Illinois State University ​(Nequals​21,000) and Population Blong dashAll residents of Homer​ Glen, IL ​(Nequals​21,000). You want to estimate the mean age of each population using two separate samples each of size nequals75. If you construct a​ 95% confidence interval for each population​ mean, will the margin of error for population A be​ larger, the​ same, or smaller than the margin of error for population​ B? Justify your reasoning.

Answer 1

Answer: the margin of error for population A would be smaller than the margin of error for population

Explanation:

The mean age of each population would vary due to the distribution of the ages of the of each population. This means that the mean would not be the same even if the population size and the number of samples taken are the same for both population. If the variation of the ages with the mean age vary widely, the standard deviation would be higher. A low standard deviation means that the ages are closer to the mean age.

In determining confidence interval, we divide the standard deviation by the square root of the number of samples. Thus, the higher the standard deviation, the higher the margin of error that would be gotten.

The ages of college students would be closer to each other and to the mean than the ages of residents. Thus, the standard deviation for the ages of college students would be smaller. Therefore,

the margin of error for population A would be smaller the margin of error for population.