Statistics 104 – Laboratory 9
This lab looks at the distribution of the sample proportion p̂ by sampling from a population of
250 statistics students. The characteristic we are interested in is the proportion of the population
with blue eyes.
1. We can simulate the construction of the sampling distribution of a sample statistic by taking
many samples (called repeated sampling) from the population and looking at the distribution
of the sample statistics obtained. Refer to the table titled “Eye Color for a Population of 250
Statistics Students.” This table contains a listing of the eye color for the population
members. Rather than list the names of the population members, this table numbers them by
rows numbered (00, 01, . . ., 09, 10, . . . , 24) and columns numbered (0,1,2,. . . , 9). For
example, student 037 (Row 03 and Column 7) has green eyes.
a) Use the random number table to select a simple random sample of 25 students from this
population. Write the student numbers and eye colors on the answer sheet. Calculate the
sample proportion of blue eyes.
Note: You can make more efficient use of 3 digit random numbers doing the following.
 For numbers between 000 and 249 go directly to the table of heights.
 For numbers between 250 and 499 subtract 250 and then go to the table of
heights.
 For numbers between 500 and 749 subtract 500 and then go to the table of
heights.
 For numbers between 750 and 999 subtract 750 and then go to the table heights.
b) Take three other random samples of size 25 from the population. This requires different
random numbers than the ones used in a). Use the JMP data table containing three
columns of random numbers generated by JMP. Note that the number 250 corresponds
to 000 (blue). You do not have to record the student numbers just simply keep track of
the eye colors on the answer sheet and calculate the sample proportion of blue eyes for
each sample. When you have finished getting your four random samples and associated
sample proportions, go to the front of the room and write your sample proportions on the
whiteboard.
This population of statistics students has a population proportion p  0.312 . We are
interested in the distribution of the sample proportion for random samples of size n  25 .
c) What is the mean of the sampling distribution of the sample proportion for samples of
size n  25 ?
d) What is the standard deviation of the sampling distribution of the sample proportion for
samples of size n  25 ?
e) Draw a histogram using the sample proportions written on the whiteboard. Describe the
shape of the distribution. Does the distribution look like a normal model? Explain
briefly.
f) If we increased the size of the sample to n  100 , describe the shape of the sampling
distribution of the sample proportion and give the mean and standard deviation.
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2. For the next part of the lab you will look at simulating drawing samples from this population
at random and investigate how different choices for the sample size and the population
proportion affect the sampling distribution of the sample proportion, p̂ . You will use the
applet on the web at
www.rossmanchance.com/applets/Reeses/ReesesPieces.html
You can get to this URL from the course web page via the link to Reese’s Pieces Simulation.
In the applet, enter 0.312 for the value of  . Note: this applet uses the Greek letter  for the
population proportion. Remember that p = 0.312 is the proportion of blue eyes in our
population of statistics students, in the simulation  = 0.312 will be the population
proportion of orange Reese’s Pieces.
a) Enter the value of 25 for sample size. Enter 60 for num samples (the number of
samples). Turn off the Animate by clicking on the check mark. Press Draw Samples
once. The applet has just done what the lab has done in activity 1. Sketch the histogram
of the 60 values of the sample proportion, p̂ . Describe the shape of the histogram. Does
it look like a normal model?
b) Press the Draw Samples enough times so that the Current Sample is 600. Click the box
next to Plot Normal Curve. Does the histogram look like a normal model? Explain
briefly.
c) Reset the Applet. Un-check the box next to Plot Normal Curve. Enter 10 in the sample
size box, 100 in the number of samples box and 0.15 for  . Click the Draw Samples
button 6 times. The Current Sample should be 600. Describe the shape of the histogram.
Click on the box next to Plot Normal Curve. Does the histogram look like a normal
model? Explain briefly.
d) Is the Success/Failure condition satisfied for p = 0.15 and n = 10? Explain briefly.
e) Reset the Applet. Un-check the box next to Plot Normal Curve. Enter 200 in the sample
size box, 100 in the number of samples box and 0.15 for  . Click the Draw Samples
button 6 times. The Current Sample should be 600. Describe the shape of the histogram.
Click on the box next to Plot Normal Curve. Does the histogram look like a normal
model? Explain briefly.
f) Is the Success/Failure condition satisfied for p = 0.15 and n = 200? Explain briefly.
g) For p = 0.15 and n = 200, what are the mean and standard deviation of the sampling
distribution of the sample proportion, p̂ ?
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Group Answer Sheet
Names of Group Members:
____________________, ____________________
____________________, ____________________
1.
a)
Number Color
Sample 1
Number Color
Number
Color
sample proportion
of blue eyes:
b)
blue
brown
green
hazel
other
sample
proportion of
blue eyes
Sample 2
p̂ =
Sample 3
p̂ =
Sample 4
p̂ =
c) What is the mean of the sampling distribution of the sample proportion for samples of
size n  25 ?
d) What is the standard deviation of the sampling distribution of the sample proportion for
samples of size n  25 ?
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e) Draw a histogram using the sample proportions on the blackboard. Describe the shape of
the distribution. Does the distribution look like a normal model? Explain briefly.
0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64
f) If we increased the size of the sample to n  100 , describe the shape of the sampling
distribution of the sample proportion and give the mean and standard deviation of that
sampling distribution.
2. For the next part of the lab you will look at simulating drawing samples from this population
at random and investigate how different choices for the sample size and the population
proportion affect the sampling distribution of the sample proportion, p̂ .
a) Sketch the histogram of the 60 values of the sample proportion, p̂ . Describe the shape of
the distribution. Does it look like a normal model?
0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64
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b) Does the histogram look like a normal model? Explain briefly.
c) Describe the shape of the histogram. Does the histogram look like a normal model?
Explain briefly.
d) Is the Success/Failure condition satisfied for p = 0.15 and n = 10? Explain briefly.
e) Describe the shape of the histogram. Does the histogram look like a normal model?
Explain briefly.
f) Is the Success/Failure condition satisfied for p = 0.15 and n = 200? Explain briefly.
g) For p = 0.15 and n = 200, what are the mean and standard deviation of the sampling
distribution of the sample proportion, p̂ .
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