A population has a mean of 200 and a standard deviation of 50. A simple random sample
of size 100 will be taken and the sample mean will be used to estimate the population mean.
a. What is the expected value (Mean) of sample mean
b. What is the standard deviation of sample mean
c. What does the sampling distribution of sample mean show?
a. To find the expected value (mean) of the sample mean, we can use the formula:
Expected value of sample mean = Population mean
In this case, the population mean is given as 200. Therefore, the expected value of the sample mean is also 200.
b. To find the standard deviation of the sample mean, we can use the formula:
Standard deviation of sample mean = Population standard deviation / Square root of sample size
In this case, the population standard deviation is given as 50 and the sample size is given as 100. Therefore, the standard deviation of the sample mean can be calculated as:
Standard deviation of sample mean = 50 / √100 = 50 / 10 = 5
Therefore, the standard deviation of the sample mean is 5.
c. The sampling distribution of the sample mean shows the distribution of all possible sample means that could be obtained from repeated sampling of the population. It provides information about the variability and behavior of the sample means compared to the population mean. In this case, the sampling distribution of the sample mean will be centered around the population mean of 200, and the standard deviation of the sample mean (5) indicates the spread or variability of the sample means.