OBJECTIVES: This lab is designed to acquaint you with the sampling distribution of the sample mean X-bar.

DIRECTIONS: Follow the instructions below in answering all the questions. Your answers should be in a form of a brief report, to be handed in to the lab instructor before you leave.
 

1.DATA: The first data we will use for this Lab will be simulated (constructed) by Minitab. Generate 50 samples each of size 10 from a normal distribution with m =10 and s =2 .

a). Calculate the mean X-bar of each sample & store all the X-bars in one column. Calculate the mean & standard deviation of the X-bars. How do they compare with those of the initial distribution. Note that the standard deviation of the X's is called the standard error.

b). Plot a histogram & a normal probability plot for the X-bars.

c). Repeat part a) by changing the sample size from 10 to 40 & 90. How are the mean & the standard deviation affected by the sample size? Comment.

d). What happens to the histogram & the normal probability plot as the sample size increases? Comment.

2. Redo problem 1 by generating samples from an exponential distribution with mean=5. The Central Limit Theorem states that the sampling distribution of the sample mean approaches normal as the sample size increases. Is this the case here? Comment.

3. Now go to the Rice Virtual Lab in Statistics (  http://www.ruf.rice.edu/%7Elane/stat_sim/sampling_dist/index.html ) and select "Begin" under "Sampling Distributions" on the left side of the page to answer the following questions. The Lab assistants will help you in accessing the Rice Virtual Lab if necessary.

a). Generate the data from a Uniform distribution. For which N is the normal distribution a good approximation to the sampling distribution of X-bar? Use 10,000 samples to get a better representation of the sampling distribution of X-bar.

b). Repeat part a) but generating data from the "skewed" distribution.