AP Statistics
Hypothesis Testing for Proportions
1. Got milk? In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults
drink milk. A regional farmers’ organization planning a new marketing campaign across its
multi-county area polls a random sample of 750 adults living there. In this sample, 657
people said that they drink milk. Do these responses provide strong evidence that the 90%
figure is not accurate for this region?
Correct the mistakes you find below in a student’s attempt to test an appropriate
hypothesis:
H0 : pˆ  0.9
HA : pˆ  0.9
SRS ,750  10
657
(0.88)(0.12)
 .876; pˆ 
 0.012
750
750
z
0.876  0.94
 2
0.012
P  value  P(z  2)  0.977
There is more than a 97% chance that the
stated percentage is correct for this
region.



Symbol should be ‘p’ for population proportion
Question does not indicate a direction of less than, “not
accurate” indicates a two-sided (not equal) alternative
Define ‘p’: p = proportion of all adults in this region who
would respond that they drink the cereal milk
Conditions must be STATED & VERIFIED

SRS: “polls a random sample of 750 adults”

Independence: We must assume that at least 7500 adults live
in this region in order to proceed

It’s not important than 750 be greater than 10. Instead we
need at least 10 expected successes and failures based on the
claimed proportion in order to assume a Normal
approximation. That is, np0 > 10 AND n(1- p0) > 10. We have
675 expected successes (750 *.9) and 75 expected failures (750
* .1). Therefore, the sampling distribution of p-hat is
approximately Normal.
Arithmetic

Label calculations: p-hat = 657/750

Show formulas before substitution

Be careful with rounding – use reported values (.876 vs. .88)

Z-score uses incorrect value for p (.94 vs. .9)

Z = (.876 -.9)/.012 = -2.19

P-value statement is incorrect, considering the alternative
hypothesis. Correct p-value: P(|z| > 2.19) = .0285
Decisions/Conclusions

P-value is incorrectly interpreted. Correct interpretation: If
an infinite number samples were from this region, we would
expect about 2.85% of those samples to show results as
extreme or more extreme than our sample.

No decision was made. We should reject the null hypothesis,
assuming that the level of significance of 5%.

We have sufficient evidence to conclude that the 90% figure is
not accurate for this region.
Choose three (3) of the following to complete. Each requires the use of a hypothesis test for
proportions. Show all work, using SCAD as your guide.
2. A magazine is considering the launch of an online edition. The magazine plans to go ahead
only if it’s convinced that more than 25% of current readers would subscribe. The magazine
contacts a simple random sample of 500 current subscribers, and 137 of those surveyed
expressed interest. What should the company do?
Nearly 100% of all samples will show that more than 25% of
current readers would subscribe. The company should
launch an online edition.
3. Census data for a certain county shows that 19% of the
adult residents are Hispanic. Suppose 72 people are called
for jury duty, and only 9 of them are Hispanic. Does this
apparent underrepresentation of Hispanics call into
question the fairness of the jury selection system?
Because p-value > alpha, we would fail to reject the null
hypothesis. This is not a significant underrepresentation.
This sample falls within the “usual” range of samples.
4. A start-up company is about to market a new computer
printer. It decides to gamble by running commercials
during the Super Bowl. The company hopes that name
recognition will be worth the high cost of the ads. The goal
of the company is that over 40% of the public recognize its
brand name and associate it with computer equipment.
The day after the game, a pollster contacts 420 randomly
chosen adults, and finds that 181 of them know that this
company manufacturers printers. Would you recommend
that the company continue to advertise during Super
Bowls?
I would recommend that the company continue to advertise during Super Bowls. Because
p-value > alpha, we would fail to reject the null hypothesis. We have sufficient evidence
to suggest that more than 40% of the public would recognize its brand name and
associate it with its computer equipment.
5. Some people are concerned that new tougher standards
and high-stakes tests adopted in many states may drive
up the high school dropout rate. The National Center for
Education Statistics reported that the high school dropout
rate for the year 2 000 was 10.9%. One school district,
whose dropout rate has always been very close to the
national average, reports that 210 of their 1782 students
dropped out last year. Is their experience evidence that
the dropout rate may be increasing?
Their experience does not provide sufficient evidence that the dropout rate may be
increasing. The p-value is greater than alpha. We would fail to reject the null hypothesis.
6. The National Center for Education Statistics monitors
many aspects of elementary and secondary education
nationwide. Their 1996 numbers are often used as a
baseline to assess changes. In 1996, 34% of students had
not been absent from school even once during the
previous month. In the 2000 survey, responses from 8302
students showed that this figure had slipped to 33%.
Officials would, of course, be concerned if student
attendance were declining. Do these figures give evidence
of a change in student attendance?
These figures do not give evidence of a chance in student attendance. The p-value is
greater than alpha. We would fail to reject the null hypothesis.