Consider the following two scenarios:
(A) Take a random sample of 50 students from an elementary school with children in K to 5th grade.
(B) Take a random sample of 50 1st grade students from the same elementary school.
For each sample, you are interested in the average height. Which of these has the smaller margin of error for 90% confidence?
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So I know margin of error = critical value * standard error of the statistics or margin of error = critcal value * standard deviation of the statistic
The heights will vary more in the scenario (A) as 5th graders are usallly taller than 1st graders, making the standard deviation in scenario (A) greater. When you multiply a constant (critical value will be the same in both scenarios) by a larger number, you will get a larger result, so thus, (B) will yield the smaller margin of error for 90% confidence.
HOW IS MY REASONING?