1. Reese’s Pieces candies have three colors: orange, brown, and yellow. Which color do you think has more
candies in a package: orange, brown or yellow? Look at website picture.
2. Guess the proportion of each color in a bag:
Orange____ Brown____ Yellow______
3. If each student in the class takes a sample of 30 Reese’s pieces, would you expect every student to have the
same number of orange candies in their sample? Explain.
4. Pretend that 10 students each took samples of 30 Reese’s pieces. Write down the number of orange candies
you might expect for these 10 samples:
___ ___ ___ ___ ___ ___ ___ ___ ___ ___
These numbers represent the variability you would expect to see in the number of orange candies in 10
samples of 30 pieces.
Review of Equations:

pˆ 
count of "successes" in sample X

size of sample
n

The mean of the sampling distribution is  p̂  p

The standard deviation of the sampling
p(1  p)
n
The standard deviation of p̂ only woks when the
distribution is  pˆ 


population is at least 10 times as large as the sample.
As a rule of thumb, use the normal approximation when n and p and (1  p) satisfy np  10 and
n(1  p)  10 .
These numbers represent the variability you would expect to see in the number of orange candies in 10
samples of 30 pieces. You will be given a bag that is a random sample of Reese’s pieces.
1. Now, count the colors for your sample and fill in the chart below:
Orange
Yellow
Brown
Number of candies
_____
_____
_____
Proportion of candies
_____
_____
_____
Write the number AND the proportion of orange candies in your sample on the board. Draw the dotplots below:
It turns out Forty-five percent of all orange candies are orange.
2. If you are given a SRS of 30 Reese’s Pieces. Determine  p̂ and  p̂ .
3. What is the probability that  p̂ will be greater than 0.45?
4. What is the probability that  p̂ will be greater than 0.75?
Imagine a very large candy machine filled with orange, brown, and yellow candies.
When you insert money, the machine dispenses a sample of candies.
Figure 7.10 The result of taking one SRS of 25 candies from a large candy machine in which 45% of the
candies are orange.
1. Launch the Reese’s Pieces® applet at our website. Notice that the population proportion of orange
candies is set to p = 0.45 (the applet calls this value π instead of p).
2. Click on the “Draw Samples” button. An animated simple random sample of n = 25 candies should be
dispensed. Figure 7.10 shows the results of one such sample. Was your sample proportion of orange
candies (look at the value of ôop in the applet window) close to the actual population proportion, p =
0.45? Why or why not?
3. Click “Draw Samples” 9 more times, so that you have a total of 10 sample results. Look at the dotplot of
your p^-values. What is the mean of your 10 sample proportions? What is their standard deviation? In
theory what should the mean and standard deviation be?
4. To take many more samples quickly, enter 390 in the “num samples” box. Click on the Animate box to
turn the animation off. Then click “Draw Samples.” You have now taken a total of 400 samples of 25
candies from the machine. Describe the shape, center, and spread of the approximate sampling
distribution of p^ shown in the dotplot.
5. How would the sampling distribution of the sample proportion p^ change if the machine dispensed n =
50 candies each time instead of 25? “Reset” the applet. Take 400 samples of 50 candies. Describe the
shape, center, and spread of the approximate sampling distribution. (in comparison to question 4)
6. How would the sampling distribution of p^ change if the proportion of orange candies in the machine
was p = 0.15 instead of p = 0.45? Does your answer depend on whether n = 25 or n = 50? Use the applet
to investigate these questions. Then write a brief summary of what you learned.
7. What if the p=.15 and your sample size was only 10? Describe the shape, center, and spread of the
approximate sampling distribution. (in comparison to question 4)