Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The standard error of the mean is
A) 24.39.
B) 28.
C) 2.
D) 1.74.

Question

Quizplus · Accepted Answer

The standard error of the mean (SEM) is calculated using the formula SEM = σ/√n, where σ is the population standard deviation and n is the sample size. Given a variance of 196, the standard deviation (σ) is the square root of 196, which is 14. The sample size (n) is 49. Therefore, SEM = 14/√49 = 14/7 = 2. However, because the population is finite and the sample size is more than 5% of the population (49 out of 200), we must apply the finite population correction (FPC), which is √((N-n)/(N-1)), where N is the population size. FPC = √((200-49)/(200-1)) = √(151/199). The corrected SEM = 2 * √(151/199), which is approximately 1.74, making D the correct choice.

Random Samples of Size 49 Are Taken from a Population