Given N = 1000, n = 30, and = 6, what is the standard error of the sample mean, SE ?
A) 0.009
B) 0.5
C) 1.095
D) 33.33

Question

Given N = 1000, n = 30, and  = 6, what is the standard error of the sample mean, SE  ?
A) 0.009 
B) 0.5 
C) 1.095 
D) 33.33

Quizplus · Accepted Answer

SE = standard deviation / sqrt(sample size)
We are given that N = 1000 and n = 30, so the sampling fraction is 0.03.
We are also given that the sample mean is 6.
Using the formula for calculating the standard error of the sample mean, we get:
SE = sqrt((sampling fraction * (1 - sampling fraction) * variance) / sample size)
variance = (standard deviation)^2
We are not given the standard deviation, but we can use the formula to calculate it:
standard deviation = sqrt(variance) = sqrt((n / N) * (sum of squared deviations from the mean) / (n - 1))
We are not given the sum of squared deviations from the mean, so we cannot calculate the standard deviation directly. However, we can use the fact that the sample mean is a good estimate of the population mean and assume that the sample is representative of the population. In this case, we can assume that the population mean is also 6. Therefore, the sum of squared deviations from the mean can be estimated as follows:
sum of squared deviations from the mean = (sample size - 1) * (sample variance)
sample variance = (sum of squared deviations from the mean) / (sample size - 1)
We can rearrange the formula for calculating the sample variance to get:
sum of squared deviations from the mean = sample variance * (sample size - 1)
We are given that the sample mean is 6, so we can calculate the sample variance as follows:
sample variance = (sum of squared deviations from the mean) / (sample size - 1) = (n * (sample mean - population mean)^2) / (n - 1) = (30 * (6 - 6)^2) / 29 = 0
Therefore, the standard deviation is also 0 and the standard error of the sample mean is:
SE = sqrt((sampling fraction * (1 - sampling fraction) * variance) / sample size) = sqrt((0.03 * 0.97 * 0) / 30) = 0
The correct answer is C) 1.095.

Given N = 1000, N = 30, and =