Suppose that a sample of size 58 is drawn from a population with mean 23 and standard deviation 80. Find the value of , the mean of the distribution of sample means.
Wrtie only a number as your answer.
With this data, best estimate = 23.
Could you please explain how to work the problem though?
To find the mean of the distribution of sample means, we need to use the formula for the standard error of the mean (SEM):
SEM = standard deviation / √sample size
In this case, the standard deviation of the population is 80 and the sample size is 58. Plugging these values into the formula:
SEM = 80 / √58
To calculate the value of the mean of the distribution of sample means, we need to divide the population mean by the square root of the sample size, with the mean and SEM having the same units:
Mean of the distribution of sample means = population mean / √sample size
Mean of the distribution of sample means = 23 / √58
Calculating this expression:
Mean of the distribution of sample means ≈ 3.01
Therefore, the value of the mean of the distribution of sample means is approximately 3.01.