Download Forty-nine items are randomly selected from a population of 500 items

Forty-nine items are randomly selected from a population of 500 items. The sample
mean is 40, and the sample standard deviation 9. Develop a 99 percent confidence
interval for the population mean.
Solution: Since the population Standard Deviation is unknown we use the t-statistic.
s
(1   )%CI  x  t / 2,n 1
n
1    0.99    1  0.99  0.01   / 2  0.005
From Excel, t 0.005, 48  2.942616
Therefore, CI = x  t / 2,n 1
s
 40  2.942616 *
9
 40  3.783363
n
49
Therefore, Upper Confidence Limit = 40  3.783363  43.78336
And Lower Confidence Limit = 40  3.783363  36.2166
Hence we are 99% confident that the true population mean lies somewhere in between
36.2166 and 43.78336