Math 160 - Cooley Intro to Statistics OCC

Section 7.2 – The Mean and Standard Deviation of the Sample Mean Mean of the Sample Mean For samples of size n, the mean of the variable x equals the mean of the variable under consideration. In symbols,

 x   Standard Deviation of the Sample Mean For samples of size n, the standard deviation of the variable x equals the standard deviation of the variable under consideration divided by the square root of the sample size. In symbols,   x  n  Exercises:

1) Refer to Exercise #1 from Section 7.1: The winner of the 2008-2009 National Basketball Association (NBA) championship was the Los Angeles Lakers. The following table provides the usual starting players and their positions and heights.

Player Position Height (in.) Trevor Ariza (T) Forward 80 Kobe Bryant (K) Guard 78 Andrew Bynum (A) Center 84 Derek Fisher (D) Guard 73 Pau Gasol (P) Forward 84

a) Determine the population mean height, μ, of the five players.  From Section 7.1, we found that m = 79.8 inches

b) Consider samples of size 4 without replacement and find the mean of the variable x .  From Section 7.1, here is the sampling distribution for samples of size 4:

Sample Heights x T, K, A, D 80, 78, 84, 73 78.75 T, K, A, P 80, 78, 84, 84 81.5 T, K, D, P 80, 78, 73, 84 78.75 T, A, D, P 80, 84, 73, 84 80.25 K, A, D, P 78, 84, 73, 84 79.75

c) Find  x , using only the result in part a).

2) According to the U.S. Bureau of Labor Statistics publication News, self employed persons with home based businesses work at a mean of 23 hours per week at home with a standard deviation of 10 hours. For samples of size 100, find the mean and standard deviation of all possible sample mean hours worked per week at home. Repeat for samples of size 1000.