AP Statistics: Part 6 Exam Breakdown
Exam breakdown: Chapters 23-25

1 Day Test (Thursday, April 16th)
o Ten Multiple Choice Questions
o 3 Short Answer Questions
Topics to be reviewed:




Inference about Means (Ch. 23)
o Vocabulary to know: degrees of freedom, one-sample t-test, one sample
t-interval
o Know the difference between the normal model and t-distribution
 Both are unimodal and symmetric
 T-model is wider than the normal model
 As degrees of freedom increases, the variability in the tdistribution decreases, causing it to become closer and closer to
the normal model
o Degrees of freedom for one mean = 𝑛 − 1
o Be able to correctly interpret a p-value and a confidence interval for one
mean
Comparing Means (Ch. 24)
o Vocabulary to know: two-sample t-test, two-sample t-interval
o Be able to correctly interpret a p-value and a confidence interval for two
means
o Know how to calculate degrees of freedom for two means in your
calculator
Paired Samples and Distinguishing the Different Tests (Ch. 25)
o Vocabulary to know: paired data, paired t-test, paired t-interval
o Be able to recognize the difference between two independent samples
and matched pairs
 Matched pairs arise from data values that come from the same
person/group/sample
o Be able to distinguish the difference between:
 Proportions vs. means
 One sample vs. two samples
 Independent two samples vs. matched pairs
 Hypothesis test vs. confidence interval
Don’t forget…
o To list all the conditions IN CONTEXT
o To define your variables (for one mean µ, for two means 𝜇1 and 𝜇2 , and
for matched pairs 𝜇𝑑 for the difference of the means)
o To show ALL WORK
o To write out all conclusions IN CONTEXT
Example Multiple Choice Questions
____1. A marketing company reviewing the length of TV commercials monitored a random
sample of commercials over several days. They found that a 90% confidence interval for the
mean length (in seconds) of commercials aired daily was (18, 31). Which is true?
A)
B)
C)
D)
E)
90% of the commercials they checked were between 18 and 31 seconds long
90% of all the commercials aired were between 18 and 31 seconds a day
Commercials average between 18 and 31 seconds long on 90% of the days
90% of all samples would show mean commercial length between 18 and 31 seconds
We’re 90% sure that the mean commercial length is between 18 and 31seconds
____2. Which statement correctly compares t-distributions to the Normal distribution?
I.
II.
III.
A) I only
t distributions are also unimodal shaped and symmetric
t distributions are more spread out than normal distribution
As degrees of freedom increase, the variance of t distributions becomes smaller
B) II only
C) I and II only
D) I and III only
E) I, II, and III
____3. A random sample of 120 classrooms at a large university found that 70% of them had
been cleaned properly. What is the standard error of the sample proportion?
A) .012
B) .042
C) .044
D) .089
E) .486
____4. A survey asked 150 random people, “On what percent of days in a week do you get more
than 8 hours of sleep per night?” The survey asked 75 men and found that 34 of them
receive more than 8 hours of sleep per night in a week, whereas 51 of the 75 women said
they receive more than 8 hours of sleep per night in a week. We want to estimate the
difference in sleep frequency between men and women. We should use a…
A) 1-proportion z-interval
D) 2-sample t-interval
B) 2-proportion z-interval
C) 1-sample t-interval
E) matched pairs t-interval
____5. A coffee house owner knows that customers pour different amounts of coffee into their
cups. She samples cups from 20 customers she believes to be representative of the
customer and weighs the cups, finding a mean of 12.5 ounces and standard deviation of .5
ounces. Assuming these cups of coffee can be considered a random sample of all cups of
coffee, which of the following formulas gives a 99% confidence interval for the mean
weight of all cups of coffee?
A)
B)
C)
D)
E)
12.5 ± 1.969(.5/√20)
12.5 ± 2.228(.5/√20)
12.5 ± 2.861(.5/√20)
12.5 ± 2.228(.5/√19)
12.5 ± 2.265(.5/√19)
____6. An elementary school principal wants to know the mean number of children in families
whose children attend this school. He checks all the families using the school’s
registration records, and we use the computer to create a 99% confidence interval based
on a t-distribution. This procedure was not appropriate. Why?
A)
B)
C)
D)
E)
Since these families are from only one school, the family sizes may be skewed
The entire population of families was gathered so there is no reason to do inference
The recent record-setting family with twelve children is probably an outlier
The population standard deviation is known, so we should have used a z-model
At a given school families are not randomly selected
____7. Doctors at a technology research facility randomly assigned equal numbers of people to
use computer keyboards in two rooms. In one room a group of people typed a manuscript
using standard keyboards, while in the other room a group of people typed a manuscript
using ergonomic keyboards to see if those people could type more words per minutes.
After collecting data for several days the researchers tested the hypothesis
𝐻0 = 𝜇1 − 𝜇2 = 0 against the one-tail alternative and found 𝑝 = .32. Which is true?
A) The people using ergonomic keyboards type 32% more words per minute
B) There’s a 32% chance that people using ergonomic keyboards type more words per
minute
C) There’s a 32% chance that there’s really no difference in typing speed
D) There’s a 32% chance another experiment will give these same results
E) None of these.
____8. Trainers need to estimate the level of fat in athletes to ensure good health. Initial tests
were based on a small sample but now the trainers double the sample size for a followup test. The main purpose of the large sample is to…
A)
B)
C)
D)
E)
Reduce response bias
Decrease the variability of the population
Reduce non-response bias
Reduce confounding due to other variables
Decrease the standard deviation of the sampling model
____9. A random sample of 64 overweight adults was chosen and their body weights were
recorded (in pounds). The adults then did 1 hour of exercise per day for 3 weeks straight.
After this period of time, their new body weights were measured and recorded. During
this time, the adults’ diets stayed the same as before as well as their sleep schedules.
Which procedure should we use to see if there is evidence that exercising for 1 hour a day
can help adults lose weight?
A) 1-proportion z-test
D) 2-sample t-test
B) 2-proportion z-test
C) 1-sample t-test
E) matched pairs t-test
____10. A contact lens wearer read that the producer of a new contact lens boasts that their
lenses are cheaper than contact lenses from another popular company. She collected some data,
then tested the null hypothesis 𝐻0 : 𝜇𝑜𝑙𝑑 − 𝜇𝑛𝑒𝑤 = 0 against the alternative 𝐻𝐴 : 𝜇𝑜𝑙𝑑 − 𝜇𝑛𝑒𝑤 > 0.
Which of the following would be a Type II error?
A)
B)
C)
D)
E)
Deciding that the new lenses are cheaper, when they really are
Deciding that the new lenses are cheaper, when in fact they are not
Deciding that the new lenses are not really cheaper, when in fact they are
Deciding that the new lenses are not really cheaper, when they really are not
Applying these results to all contact lenses, new and old
Example Short Answer Questions
1. Suppose you were asked to analyze each of the situations described below. (NOTE: Do not
actually do these problems!) For each, indicate what procedure you would use, the test statistic (z
or t), and if t, the number of degrees of freedom. If you need the calculator to calculate the
degrees of freedom, write “calculator”. If the procedure uses z, just write N/A for the degrees of
freedom. Record your answers into the chart below based off of the scenarios given below.
Proportion or Mean?
One or Two Samples?
a.
b.
c.
d.
e.
f.
Z or T?
Degree of Freedom?
2.
Every year, Educational Services selects readers for the AP Exams. Recently the AP Stats exam
has been graded in Lincoln, Nebraska. One objective of ETS is to achieve equity in grading by
inviting teachers to be readers from all parts of the nation. However budgets are a consideration
also. The accountants at Educational Services wonder if the flights from cities west of Lincoln are
the same as flight costs from cities east of Lincoln. A random sample of the expense vouchers
from last year was reviewed for the cost of airline tickets. Costs (in dollars) are shown in the
table.
a. Test an appropriate hypothesis and state your conclusion.
b. Create a 95% confidence interval to support your claim in part a. Be sure to state your
conclusion in context.
3.
4.
Test an appropriate hypothesis and state your conclusion.
Part VI Review Book Problems
Directly after the chapter 25 book problems, your textbook contains the Part VI Review
problems. The complete solutions to ALL of these problems can be found under the
“Part VI” tab on the class website: www.myhaikuclass.com/hjhunt/apstats. It is on the
side of the page called “Part VI Review Book Solutions”. Here is a breakdown of the
problems and what content each covers. Please focus on the material that you feel you
need the most help/practice in. It’s a good idea to hit each concept but to practice the
content you struggle most with, even more.
Example Multiple Choice Questions – Solutions
1) E 2) E 3) B 4) B 5) C 6) B 7) E 8) E 9) E 10) C