The Practice of Statistics – 9.2 examples
I’m a Great Free-Throw Shooter! (page 565)
Checking conditions
Check the conditions for performing a significance test of the virtual basketball player’s claim.
I’m a Great Free-Throw Shooter! (page 556-557)
Computing the test statistic
In an SRS of 50 free throws, the virtual player made 32.
(a) Calculate the test statistic.
(b) Find the P-value using Table A or technology. Show this result as an area under a standard Normal curve.
One Potato, Two Potato (page 559)
Performing a significance test about p
The potato-chip producer of Section 9.1 has just received a truckload of potatoes from its main supplier. Recall that
if the producer finds convincing evidence that more than 8% of the potatoes in the shipment have blemishes, the
truck will be sent away to get another load from the supplier. A supervisor selects a random sample of 500 potatoes
from the truck. An inspection reveals that 47 of the potatoes have blemishes. Carry out a significance test at the
 = 0.05 significance level. What should the producer conclude?
STATE:
PLAN:
DO:
CONCLUDE:
Nonsmokers (page 562)
A two-sided test
According to the Centers for Disease Control and Prevention (CDC) Web site, 50% of high school students have never
smoked a cigarette. Taeyeon wonders whether this national result holds true in his large, urban high school. For his
AP® Statistics class project, Taeyeon surveys an SRS of 150 students from his school. He gets responses from all 150
students, and 90 say that they have never smoked a cigarette. What should Taeyeon conclude? Give appropriate
evidence to support your answer.
STATE:
PLAN:
DO:
CONCLUDE:
Nonsmokers (page 563)
A confidence interval gives more info
Taeyeon found that 90 of an SRS of 150 students said that they had never smoked a cigarette. We checked the
conditions for performing the significance test earlier. Before we construct a confidence interval for the population
proportion p, we should check that both n p̂ and n (1 − p̂ ) are at least 10.
n
p̂ =
n (1 −
p̂
)=
Our 95% confidence interval is
Perfect Potatoes (page 565-566)
Type II error and power
The potato-chip producer wonders whether the significance test of H0: p = 0.08 versus Ha: p > 0.08 based on a
random sample of 500 potatoes has enough power to detect a shipment with, say, 11% blemished potatoes. In this
case, a particular Type II error is to fail to reject H0: p = 0.08 when p = 0.11. Figure 9.10 shows two sampling
distributions of p̂ , one when p = 0.08 and the other when p = 0.11.
Figure 9.10 In the bottom graph, the
power of the test (shaded area) is the
probability that it correctly
rejects H0: p = 0.08 when the truth
is p = 0.11. In this case, power =
0.7626. The probability of making a
Type II error (white area) is 1 −
0.7626 = 0.2374.