Suppose you have two populations: population along dashall students at a state college (nequals21,000) and population blong dashall residents of a town in the state (nequals21,000). 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.

See the explantion below

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

We know that the margin of error for a confidence interval is given by:

  (1)

If we see the formula (1) at the same confidence level, for example 95% and with the same sample size the margin of error just depends of the deviation. If the population deviation for population A is higher than the population deviation for B then A will have more margin of error than B.

On the other case if the deviation for population A is lower than the deviation for population B, then we will have less margin of error for population A than population B.

And the other possible case if both population have the same deviation, then both have equal margin of error.  

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