Name: ______________________________________________ Date: ____________________ Pd: ______
Activity – Confidence Intervals Lab
What is the proportion (percentage)
of white beads in the bag?
Step 1: Guess. What percentage of the beads in the bag do YOU think are white?
_______
Step 2: Sampling


Examine your sample. (Please be careful and don’t lose any beads!!!)
Count and record your findings.
Sample Size (n): _______
Number of White Beads (x): _______
Step 3: Calculate Point Estimate

Calculate the point estimate for p, the true proportion of white beads in the bag.
𝑝̂ =
𝑥
𝑛
= ______ = _______
𝑞̂ = 1 − 𝑝 = ________
Step 4: Calculate Margin of Error and Confidence Interval
Error:

𝐸 = 𝑧𝑐 √
𝑝̂∙𝑞̂
𝑛
Use a confidence level of 95%.
𝑧𝑐 =________

Use a confidence level of 99%.
𝑧𝑐 =________
© Amanda Leahy, 2016
Confidence Interval:
𝑝̂ − 𝐸 ≤ 𝑝 ≤ 𝑝̂ + 𝐸
PRIOR KNOWLEDGE: Students know how to calculate a
confidence interval for a proportion.
For this activity, I use a large gallon zip bag filled with
multicolored perler beads. I carry the bag around the
room so that each student can look and make a guess of
what percentage of white beads are in the bag.
Prior to the activity, I have ACTUALLY counted the beads
and know the percentage.
I have student come to the front of the room. I shake
the bag, reach in for a handful, and put it in a paper bowl
or in a small sandwich sized zip bag. Repeat for each
student. Students could also work in groups for this
activity.
Step 5: Class Results Recording
Go to the dry erase board and record your findings in the indicated locations.
 Sample size (n)
 Number of white beads in sample (r)
Partition off a section of your dry erase
 Confidence Interval 95%
board for each piece of data to be recorded.
 Confidence Interval 99%
Step 6: Final Results

What is the true proportion of white beads in the bag?
Total Population Size = ∑ 𝑛 = __________
True Proportion of White Beads = 𝑝 =

∑𝑥
∑𝑛
Total White Beads = ∑ 𝑥 = ___________
= ____________
What Percentage of the 95% Confidence Levels contained the true proportion?
Answers vary. I announce the “true proportion” and circle all the correct intervals.

What Percentage of the 99% Confidence Levels contained the true proportion?
Answers vary. There will be more correct intervals now. Point out that as confidence
level increases, so does the margin of error, widening the confidence interval.

What if you wanted to GUARANTEE a 99% confidence interval within 0.01 of the proportion?
What sample size would you have needed?
1 𝑧𝑐 2
𝑛= ( )
4 𝐸

n = ¼ (2.58/.01)^2 = 16641
Expect groans from students. This is a LOT of beads.
THINK ABOUT IT. Look back at your guess from Step 1 and your confidence intervals from Step 4.
Did any of your confidence intervals contain your guess? How close was your guess to the true
proportion found above using all the classroom data?
Step 7: Clean up time!
CAREFULLY return your beads to the large bag of beads. Place your empty small Ziploc bag on the front table.
© Amanda Leahy, 2016