A sample of n-25 students is selected from a population with mu =100 with standard deviation of 20. On average, how much error would be expected between the sample mean and the population mean? A. 25 pts. B. 20 pts. C 4 pts. D 0.8 pts.
Take standard deviation and divide by the square root of the sample size.
To determine the average error between the sample mean and the population mean, we need to calculate the standard error of the mean (SEM). The SEM is a measure of how much the sample means typically deviate from the population mean.
The formula for SEM is: SEM = standard deviation / √(sample size)
In this case, the standard deviation is 20 and the sample size is n-25, which means we have (n - 25) students in the sample. Since the question doesn't provide the value of n, we can't calculate the exact SEM. However, we can still determine an approximate range for the SEM.
To calculate the range, we need to consider the two extreme cases: the smallest sample size possible (n=25) and the largest sample size possible (n=infinity). Let's calculate the SEM for these two cases:
Smallest sample size (n=25):
SEM = 20 / √(25 - 25) = 20 / 0 = undefined
Largest sample size (n=infinity):
SEM = 20 / √(infinity - 25) = 20 / √(infinity) = 0
As we can see, the SEM can range from undefined to 0, depending on the sample size. Therefore, none of the answer choices provided (A, B, C, or D) can be considered accurate.
In conclusion, without knowing the exact sample size (n), we cannot determine the average error between the sample mean and the population mean in this scenario.