Question

A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean will be used to estimate the a. What is the expected value of x? b. What is the standard deviation of x? c. 18. population mean Show the sampling distribution of x What does the sampling distribution of i show?

Answer 1

Given that mean = mu = 200 standard deviation = sigma = 50 n = 100 a) The expected value of x^- is mu x^- = 200 b) The standard deviation of x^- is 6 x^- = sigma/squareroot n = 50/squareroot 100 = 50/10 = 5 c) The sampling distribution of x^- is 6 x^- = 5 d) x^- ~ N(mu x^-, 6 x^-) mu x^- = mu 6 x^- = 6/squareroot n sample mean = x^-