Exhibit 22-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 22-3. An approximate 95% confidence interval for the population mean is
A)395 to 405
B)380 to 420
C)360 to 440
D)390 to 410

Question

Quizplus · Accepted Answer

We can use the formula: 
CI = sample mean ± (tCritical * (sample standard deviation /√sample size))
where tCritical for a 95% confidence level with 57 degrees of freedom (58-1) is approximately 2.002.

Plugging in the values: 
CI = 400 ± (2.002 * (40/√58))
CI = 400 ± 10.92
CI = (400-10.92 , 400+10.92)
CI = (389.08 , 410.92)

So the best choice is D: 390 to 410 as it is the only choice that contains the entire confidence interval.

Exhibit 22-3 From a Population of Size 600, a Simple Random Sample