your job is to determine the sampling distribution of a mean of N waiting times across all hospitals

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Your job is to determine the sampling distribution of a mean of N waiting times across all

hospitals. You are aware that the population distribution is right skewed where waiting for 32

hours is very rare.

In this experiment, you will investigate the probability distribution of a sample mean for samples

of size =2, 5, and 25 number of waiting times. In doing so, you will observe the Central Limit

Theorem (see Lecture Notes) in action and learn to explain it to a lay person. The distribution of

a sample statistic (here the sample mean) is referred to as a “sampling distribution.”

i. Getting started: Go to the following web site:

http://onlinestatbook.com/stat_sim/sampling_dist/index.html

You will use the applet to generate random numbers from a true population distribution, here the

uniform distribution on the interval (0, 32)

When the page comes up, wait for the “Begin” button to appear. Click “Begin” to open the site.

When the site (“applet”) opens, notice that there are 4 sections with graphs labeled “Parent

Population”, “Sample Data”, “Distribution of Means” and a fourth graph that is not labeled.

Click on the menu at the upper right (“Normal”) in the first section, and select “Skewed.” Notice

how the shape of the graph labeled “Parent Population” changes. Below, where it says “N=5"

(under “Mean”), click the menu and change the selection to “N=2.” Now, you are ready to do the

next step ii.

PLEASE NOTE: In this applet, N refers to sample size which we denote in class as n.

ii. Means of samples of size n=2:

Click “Animated Sample.” This will generate a sample of two random waiting times that will

appear in the second graph labeled “Sample Data.” Notice that the mean of the two times is

given to the left of that graph, and a small “mass of probability” is added at its value in the third

graph labeled “Distribution of Means,” just below.

Repeat the step above for a total of 20 times by continuing to click “Animated Sample” 19 more

times to form a histogram of mean values.

Describe the shape of the histogram of means recorded by the applet in the third graph. Record

and report the mean and standard deviation of the distribution of means for n=2.

iii. Means of samples of size n=5:

Attachments:

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