Question

If two samples A and B had the same mean and standard deviation, but sample A had a larger sample size, which sample would have the wider 95% confidence interval? Sample A as it comes first Sample B as its sample is more dispersed Sample A as it has the larger sample Sample B as it has the smaller sample

Answer 1

Answer: Sample B as it has the smaller sample (choice #4)

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Explanation:

Recall that the margin of error (MOE) is defined as

MOE = z*s/sqrt(n)

The sample size n is located in the denominator, meaning that as n gets bigger, the MOE gets smaller. The same happens in reverse: as n gets smaller, the MOE gets bigger.

Put another way, a small sample size means we have more error because small samples mean they are less representative of the population at large. The bigger a sample is, the better estimate we will have of the parameter.

We are told that "sample A had a larger sample size" indicating that sample A has a more narrow confidence interval.

Therefore, sample B would have a wider confidence interval.

This is true regardless of what the confidence level is set at.