In developing an interval estimate for a population mean,a sample of 50 observations was used.The interval estimate was 19.76 ± 1.32.Had the sample size been 200 instead of 50,the interval estimate would have been:
A)19.76 ± .33
B)19.76 ± .66
C)19.76 ± 5.28
D)None of these choices.

Question

Quizplus · Accepted Answer

The formula for calculating the margin of error is:
Margin of error = (critical value) * (standard error)
The critical value depends on the level of confidence and the sample size. As the sample size increases, the critical value decreases because the standard error decreases. Therefore, if the sample size had been 4 times larger (i.e. 200 instead of 50), the critical value would have been 2 times smaller (approximately). Since the margin of error is proportional to the critical value, it would also have been 2 times smaller (approximately). Therefore, the interval estimate would have been:
19.76 ± (1.32/2) = 19.76 ± 0.66
The correct choice is B.

In Developing an Interval Estimate for a Population Mean,a Sample