Question

Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 90% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 95% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original?

Answer 1

Using confidence interval concepts, according to the margin of error, the 90% confidence interval would be narrower than the 95% confidence interval.

The margin of error of a confidence interval is given by:

• m = z a/n

In which:

z is the critical value.

is the population standard deviation.

n is the sample size.

The higher the margin of error, the wider the interval is.

The lower the confidence interval, the lower the critical value is. Hence, a 90% confidence interval has a lower critical value than a 95% confidence interval, leading to a smaller margin of error and a narrower interval

Answer 2

In general, a confidence interval with a higher confidence level will be wider than a confidence interval with a lower confidence level. This is because a higher confidence level corresponds to a larger margin of error, which leads to a wider confidence interval.

Therefore, if you calculate a 95% confidence interval, the new confidence interval will be wider than the original 90% confidence interval. This is because the 95% confidence interval will have a larger margin of error, which will cause the confidence interval to be wider.

It's worth noting that the width of a confidence interval depends on the sample size, the standard deviation of the population, and the confidence level. If the sample size or the standard deviation changes, the width of the confidence interval may also change, even if the confidence level remains the same.