Question

Marcia and Greg are each attempting to estimate the average family size of the households in their neighborhood. They each select a different random sample of 50 households. Both of their samples end up having the same sample mean, but Marcia's sample has a much smaller sample standard deviation than Greg's sample. If Marcia and Greg each use their sample data to construct a 95% confidence interval, who will have the wider confidence interval? Greg Both intervals will have the same width since the sample sizes and sample means are the same. Both intervals will have the same width since the sample sizes, sample means, and confidence levels are all the same. Marcia Both intervals will have the same width because they are both 95% confidence intervals.

Answer 1

We know that,

Larger the sample standard deviation, wider the confidence interval.

Here, Greg has sample with larger sample standard deviation and hence, wider confidence interval.

i.e., First option is correct.

Thank you.

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