In developing an interval estimate for a population mean,a sample of 40 observations was used.The interval estimate was 28.76 ± 1.48.Had the sample size been 160 instead of 40,the interval estimate would have been:
A)28.76 ± 0.37
B)28.76 ± 0.74
C)28.76 ± 1.48
D)28.76 ± 2.96

Question

Quizplus · Accepted Answer

The formula for a confidence interval for the mean is: 
CI = sample mean ± (t-score)*(standard deviation/square root of sample size)
As the sample size increases, the standard deviation/square root of sample size decreases. This means that the margin of error (t-score * standard deviation/square root of sample size) decreases as well. 
So, when the sample size is larger (160 instead of 40), the margin of error would be smaller. We can calculate the new margin of error using the formula above: 
New margin of error = 1.48 * (square root of (40/160)) = 0.74 
So, the new interval estimate would be: 
28.76 ± 0.74

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