Question

A consumer group selected 100 different airplanes at random from each of two large airlines. The mean seat width for the 100 airplanes was calculated for each airline, and the difference in the sample mean widths was calculated. The group used the sample results to construct a 95 percent confidence interval for the difference in population mean widths of seats between the two airlines.

Suppose the consumer group used a sample size of 50 instead of 100 for each airline. When all other things remain the same, what effect would the decrease in sample size have on the interval?
A. The width of the confidence interval would decrease.
B. The width of the confidence interval would increase.
C. The width of the confidence interval would remain the same.
D. The level of confidence would increase.
E. The level of confidence would decrease.

Answer 1

B. The width of the confidence interval would increase.

Explanation:

The margin of error for a confidence interval has the following format:

`M = z*(\sigma)/(√(n))`

In which z is the critical value related to the confidence level,
`\sigma` is the standard deviation of the population and n is the size of the sample.

In this problem:

The only change is that n is decreased.

From the equation above, as n decreases, the margin of error increases. A higher margin of error means that the width of the confidence interval increases.

So the correct answer is:

B. The width of the confidence interval would increase.