Question

You have two samples with a mean of 2.43. The first sample has a 95% confidence interval of 1.54-3.32 and the second sample as a 95% confidence interval of 2.00-2.86. What is one thing that must be true?

Answer 1

From the formula, it should be clear that: The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases.

So there are following possibilities:

1.sample size of first sample is smaller than that of second and standard deviation is same.

2.sample size is same and standard deviation of first sample is more than that of second sample.

3.sample size of first sample is smaller than that of second and standard deviation of first sample is more than that of second sample.