Name:____________________________________________
STT 1600 Lab 7: Confidence Intervals for Proportions
Purpose: To gain experience computing confidence intervals for proportions. This lab involves
a class activity involving all the students. Fill out this sheet and turn it in.
Confidence Intervals for a Proportion. Each student will flip a penny n=50 times and their lab
partner will record the number of heads.
1. If p=probability the penny comes up heads when flipped, what is p? p = ___________
2. From your n=50 flips, compute p̂, the proportion of heads from your 50 flips: p̂ = ______
3. For a 95% confidence level, find the z-critical value. To do this, click in an empty cell and
type “=NORMSINV(0.975)”. (We use 0.975 because, α = .05. Since we are working with
a confidence interval, we divide α by 2. Therefore we get .05/2 = .025. But the
normsinv uses the area to the left of the positive critical value, which gives us 1 - .025 =
.975.)
z-critical value = __________________
4.
For a 95% confidence interval for p, the margin of error E is given by
E = 𝑧 α √p̂(1 − p̂)/n (using p̂ from your answer in #2)
2
Compute E from your 50 flips.
E = __________________
5. Compute your 95% confidence interval
Lower Limit p̂ - E = ____________ Upper Limit p̂ + E = ______________
6. Does your confidence interval contain the true value of p? (circle one) YES NO
Each student will now tell the instructor how many heads they got out of n=50 flips and the
instructor will record these in Excel in column A. The instructor will now compute each
student’s confidence interval by doing the steps below. Each lab group can do these steps too
as follows. Suppose there are 30 students and the number of heads is recorded in rows
A1:A30.
a) In cell E1, type 50.
b) To compute the sample proportions p̂ (and put them in column B) click in cell B1 to
highlight it and in the formula ribbon type “=A1/$E$1” and hit enter. Now click in the
bottom right of cell B1 and drag your mouse to the last row of data (e.g. row 30 if there
are 30 students). Column B now has the sample proportion of heads for all the
students. Note that you need to use the “$” to get the formula to work for all rows of
data.
c) Compute the lower limits of the confidence intervals: click in cell C1 and type
“=B1-1.96*SQRT(B1*(1-B1)/$E$1)”. After this, point and click the lower right of cell C1
and drag it to the last row of data.
d) Repeat step (c) to get the upper limit of the confidence intervals by clicking in cell D1
and typing “=B1+1.96*SQRT(B1*(1-B1)/$E$1)”.
7. Approximately, what percentage of the confidence intervals should contain the true
value of p? _______________
8. What is the actual proportion of confidence intervals that contain p? __________