From a population of size 600, a simple random sample of size 60 is selected. The sample mean is 400, and the sample standard deviation is 50. An approximate 95% confidence interval for the population mean is
A) 395 to 405
B) 380 to 420
C) 360 to 440
D) 388 to 412

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the population mean when the sample size is large where:

CI = sample mean ± z* (sample standard deviation / sqrt(sample size))

With 95% confidence, the z-value is approximately 1.96. Plugging in the values provided, we get:

CI = 400 ± 1.96 * (50 / sqrt(60))
   = 400 ± 12.81
   = (387.19, 412.81)

Therefore, the best choice is D, with a 95% confidence interval of (388, 412).

From a Population of Size 600, a Simple Random Sample