A random sample of 64 items is selected from a population of 400 items.The sample mean is 200. The population standard deviation is 48.From this data,a 95% confidence interval to estimate the population mean can be computed as _______.
A) 189.21 to 210.79
B) 188.24 to 211.76
C) 190.13 to 209.87
D) 190.94 to 209.06
E) 193.45 to 211.09

Question

Quizplus · Accepted Answer

The formula for a 95% confidence interval for the population mean is:sample mean +/- 1.96 * (population standard deviation / square root of sample size)Plugging in the given values, we get:200 +/- 1.96 * (48 / square root of 64)= 200 +/- 1.96 * (48 / 8)= 200 +/- 1.96 * 6= 200 +/- 11.76= (188.24, 211.76)Therefore, the correct answer is B) 188.24 to 211.76.

A Random Sample of 64 Items Is Selected from a Population