AP Statistics
Name: _____________________
Penny Activity
Is a penny fair? Is one side of a penny heavier?
Using a coin to randomly determine an outcome, most people would flip a coin. Is it equivalent to hold the
coin vertically on a tabletop and spin the coin with a quick flick of your finger? In this activity, we will try a
third variation. We will stand pennies on edge and then bang the table to make the pennies fall. We are
interested in the proportion of times the pennies fall heads up. If the pennies are equally heavy on both sides
of the coin, then it would be reasonable to expect the long-term proportion of heads to be about 0.5. We
state the following hypothesis:
H o : p  0.5 , H a : p  0.5
Procedure:
1. Stand 20 pennies on edge on a horizontal tabletop. Take your time – this may take a steady hand and
some practice.
2. Bang the table just hard enough to make all of the pennies fall.
3. Count the number of heads that fall heads up.
4. Combine your results with those of other students in the class.
(a) Calculate the proportion of heads you obtained.
(b) Use your calculator to test the null hypothesis H o : p  0.5 , H a : p  0.5 . What is the p-value?
(c) Fill out the chart for class data below.
Student 1
2
3
4
5
6
7
x
n
8
9
10
11
12
13
14
15
16
(d) Find the proportion of heads for your entire class. What is n? Using the same null and alternate
hypothesis, find the new P-value, and compare this with the value you obtained in (b).
Totals
(e) Using the data from your experiment (not the class data), find the 95% confidence interval for the true
proportion of heads obtained.
(f) Sketch the confidence intervals for each person in the class below.
y
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
x
(g) Looking at the confidence intervals for the entire class, make a conjecture about the 95% confidence
intervals for the whole class.
(h) Use the cumulative data collected by the whole class to calculate the 95% confidence interval. Compare
this interval with your conjecture in (g). Also, compare your individual confidence interval with the
confidence interval for the whole class.
(i) Does your confidence interval contain 0.5 (the value that we used for our hypothesis test)? Why or why
not? What does this tell you about your hypothesis test?
(j) Interpret the whole class confidence interval in the context of the problem.