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. The expected value (mean) of the sample mean is equal to the population mean, which is 200. This means that if we take multiple random samples, the average of the sample means will be around 200.
b. The standard deviation of the sample mean (also known as the standard error) can be calculated using the formula:
Standard Deviation of Sample Mean = Standard Deviation of Population / Square Root of Sample Size
In this case, the standard deviation of the population is 50 and the sample size is 100. Plugging these values into the formula:
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 a given population. It is a theoretical distribution that helps us understand the variability of sample means and how they are distributed around the population mean. By considering the sampling distribution, we can estimate the range of values within which the true population mean is likely to fall.