Practice Test 12
AP Statistics
Name:
Directions: Work on these sheets. Answer completely, but be concise. Tables are attached.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. What is the value of t * , the critical value of the t distribution with 8 degrees of freedom, which
satisfies the condition that the probability is 0.10 of being larger than t * ?
(a) 1.415
(b) 1.397
(c) 1.645
(d) 2.896
(e) 0.90
2. You read in the report of a psychology experiment that “separate analyses for our two groups of 12
participants revealed no overall placebo effect for our student group (mean = 0.08, SD = 0.37,
t(11) = 0.49) and a significant effect for our non-student group (mean = 0.35, SD = 0.37, t(11) =
3.28, p < 0.01).” Are the two values given for the t test statistic correct? (The null hypothesis is
that the mean effect is zero.)
(a) Yes, both are correct.
(b) The t statistic for the student group is correct, but the one for the non-student group is incorrect.
(c) The t statistic for the non-student group is correct, but the one for the student group is incorrect.
(d) Both t statistics are incorrect.
(e) We can’t tell whether either t statistic is correct, because we aren’t given the actual data.
3. A sociologist is studying the effect of having children within the first two years of marriage on the
divorce rate. Using hospital birth records, she selects a random sample of 200 couples who had a
child within the first two years of marriage. Following up on these couples, she finds that 80
couples are divorced within five years.
To determine if having children within the first two years of marriage increases the divorce rate we
should test
(a) hypotheses H0: p = 0.50, Ha: p  0.50.
(b) hypotheses H0: p = 0.50, Ha: p > 0.50.
(c) hypotheses H0: p = 0.50, Ha: p < 0.50.
(d) hypotheses H0: p = 0.40, Ha: p > 0.40.
(e) none of the above.
4. In order to study the amounts owed to a particular city, a city clerk takes a random sample of 16
files from a cabinet containing a large number of delinquent accounts and finds the average amount
x owed to the city to be $230 with a sample standard deviation of $36. It has been claimed that the
true mean amount owed on accounts of this type is greater than $250. If it is appropriate to assume
that the amount owed is a Normally distributed random variable, the value of the test statistic
appropriate for testing the claim is
(a)  3.33
Chapter 12
(b)  1.96
(c)  2.22
1
(d)  0.55
Practice Test 12
(e)  2.1314
5. The water diet requires one to drink two cups of water every half hour from when one gets up until
one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to
test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The
weights (in pounds) are
Person
Weight before the diet
Weight after six weeks
1
180
170
2
125
130
3
240
215
4__
150
152
For the population of all adults, assume that the weight loss after six weeks on the diet (weight before
beginning the diet – weight after six weeks on the diet) is Normally distributed with mean µ. To
determine if the diet leads to weight loss, we test the hypotheses
H0:  = 0, Ha:  > 0
Based on these data we conclude that
(a) we would not reject H0 at significance level 0.10.
(b) we would reject H0 at significance level 0.10 but not at 0.05.
(c) we would reject H0 at significance level 0.05 but not at 0.01.
(d) we would reject H0 at significance level 0.01.
(e) the sample size is too small to allow use of the t procedures.
6. A random sample of 100 voters in a community produced 59 voters in favor of Candidate A. The
observed value of the test statistic for testing the null hypothesis H 0 : p  0.5 versus the alternative
hypothesis H a : p  0.5 is
(a) z   0.59  0.5
(c) t   0.59  0.5
(0.59)(0.41) 100 
(0.59)(0.41) 100 
(b) z   0.59  0.5
(d) t   0.59  0.5
(0.5)(0.5) 100 
(0.5)(0.5) 100 
(e) None of these
7. An opinion poll asks a simple random sample of 100 college seniors how they view their job
prospects. In all, 53 say “good.” Does the poll give reason to conclude that more than half of all
seniors think their job prospects are good? The hypotheses for a test to answer this question are
(a) H0: p = 0.5, Ha: p > 0.5.
(b) H0: p > 0.5, Ha: p = 0.5.
(c) H0: p = 0.5, Ha: p  0.5.
(d) H0: p = 0.5, Ha: p < 0.5.
(e) H0: p  0.5, Ha: p > 0.5.
8. In a test of H0: p = 0.4 against Ha: p  0.4, a sample of size 100 produces z = 1.28 for the value of
the test statistic. Thus, the P-value (or observed level of significance) of the test is approximately
equal to:
(a) 0.90
(b) 0.40
(c) 0.05
(d) 0.20
(e) 0.10
Chapter 12
2
Practice Test 12
9. The water diet requires one to drink two cups of water every half hour from when one gets up until
one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to
test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The
weights (in pounds) are
Person
1
2
3
4
Weight before the diet
180
125
240
150
Weight after six weeks
170
130
215
152
For the population of all adults, assume that the weight loss after six weeks on the diet (weight
before beginning the diet – weight after six weeks on the diet) is Normally distributed with mean
 . To determine if the diet leads to weight loss, we test the hypotheses
H0: µ = 0 vs. Ha: µ > 0
Based on these data we conclude that
(a)
(b)
(c)
(d)
(e)
we would not reject
we would reject H 0
we would reject H 0
we would reject H 0
none of these
H 0 at significance level 0.10.
at significance level 0.10 but not at level 0.05.
at significance level 0.05 but not at level 0.01.
at significance level 0.01.
10. Refer to the previous question. A Type II error in this setting would mean
(a) concluding that the diet leads to weight loss when it doesn’t.
(b) concluding that the diet leads to weight loss when it really does.
(c) concluding that the diet doesn’t lead to weight loss when it does.
(d) concluding that the diet doesn’t lead to weight loss when it really doesn’t.
(e) rejecting H 0 when H 0 is actually true.
The next two questions refer to the following situation.
A group of nutritionists is hoping to prove that a new soybean compound has more protein per gram
than roast beef, which has a mean protein content of 20. A random sample of 5 batches of the soy
compound have been tested, with the following results:
protein content
15, 22, 17, 18, 23
11. What assumption(s) do we have to make in order to carry out a legitimate statistical test of the
nutritionists’ claim?
(a) The observations are from a Normally distributed population.
(b) The mean protein content of the 5 batches follows a Normal distribution.
(c) The variance of the population is known.
(d) Both (a) and (b) must be assumed.
(e) All of (a), (b), and (c) must be assumed.
Chapter 12
3
Practice Test 12
12. What are the appropriate statistical hypotheses and the observed value of the corresponding test
statistic?
(a) H0: µ = 20 vs. Ha: µ < 20 and t* = 19  20 
11.5 / 5
(b) H0: µ = 20 vs. Ha: µ > 20 and t* = 19  20 
11.5 / 5
(c) H0: µ = 20 vs. Ha: µ > 20 and z* = 19  20 
11.5 / 5
(d) H0: µ = 20 vs. Ha: µ < 20 and z* = 19  20 
(e) None of these is correct.
11.5 / 5
The next two questions refer to the following situation.
In some mining operations, a by-product of the processing is mildly radioactive. Of prime concern is
the possibility that release of these by-products into the environment may contaminate the freshwater
supply. There are strict regulations for the maximum allowable radioactivity in supplies of drinking
water, namely an average of 5 picocuries per liter (pCi/l) or less. However, it is well known that even
safe water has occasional hot spots that eventually get diluted, so samples of water are assumed safe
unless there is evidence to the contrary. A random sample of 25 specimens of water from a city’s water
supply gave a mean of 5.39 pCi/l and a standard deviation of 0.87 pCi/l.
13. The appropriate null and alternative hypotheses are
(a) H0: µ = 5.39 vs Ha: µ 5.39
(b) H0: µ = 5.39 vs Ha: µ < 5.00
(c) H0: µ = 5 vs Ha: µ = 5.39
(d) H0: µ = 5 vs Ha: µ < 5
(e) H0: µ = 5 vs Ha: µ > 5
14. The values of the test statistic and the P-value (computed by a computer) are
(a) z* = 2.24; P-value = 0.0125
(b) z* = 2.24; P-value = 0.0250
(c) t* = 2.24 ; P-value = 0.0171
(d) t* = 2.24 ; P-value = 0.0173
(e) t* = 2.24 ; P-value = 0.0346
15. A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and
asked to determine if the card was one of five symbols: a star, cross, circle, square, or three wavy
lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly
identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as an SRS
from the population of all guesses the psychic would make in his lifetime. Which inference
procedure would you use to determine whether the psychic is doing better than just guessing?
(a) one-proportion z test
(b) one-sample t test
(c) one-sample z test
(d) one-proportion z interval
(e) one-sample t interval
Chapter 12
4
Practice Test 12
Part 2: Free Response
Communicate your thinking clearly and completely.
9. Many mutual funds compare their performance with that of a benchmark, an index of the returns
on all securities of the kind the fund buys. The Vanguard International Growth Fund, for example,
takes as its benchmark the Morgan Stanley EAFE (Europe, Australasia, Far East) index of overseas
stock market performance. Here are the percent returns for the fund and for the EAFE from 1982
(the first full year of the fund’s existence) to 2000.
Does the fund significantly outperform its benchmark? Carry out an appropriate test and state your
conclusion about the fund’s performance.
Chapter 12
5
Practice Test 12
10. Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal
means that the paper will live forever in libraries. The British Medical Journal combines the two: it
prints short and readable versions, with longer versions available online. Is this OK with authors?
The journal asked a random sample of 104 of its recent authors several questions. One question
was “Should the journal continue using this system?” In the sample, 72 said “Yes.”
(a) Do the data give good evidence that more than two-thirds (67%) of authors support continuing
this system? Carry out an appropriate test to help answer this question.
(b) What proportion of all authors would say “Yes” if asked? (Estimate with 95% confidence.)
Chapter 12
6
Practice Test 12
11. In a study of the effectiveness of weight-loss programs, 47 subjects who were at least 20% overweight
took part in a group support program for 10 weeks. Private weighings determined each subject’s
weight at the beginning of the program and 6 months after the program’s end. The paired t test was
used to assess the significance of the average weight loss. The paper reporting the study said, “The
subjects lost a significant amount of weight over time, t(46) = 4.68, P < 0.01.”
(a) What hypotheses were tested in this study? Be sure to define any parameters you use.
(b) Discuss whether each of the required conditions for using the paired t test is satisfied in this study.
(c) The paper follows the tradition of reporting significance only at fixed levels such as  = 0.01. In
fact the results are more significant than “P < 0.01” suggests. What is the P-value of this t test?
(d) Explain to someone who knows no statistics but is interested in weight-loss programs what the
practical conclusion is.
Chapter 12
7
Practice Test 12
12. To profitably produce a planned upgrade of a software product you make, you must charge
customers $100. Are your customers willing to pay this much? You contact a random sample of 40
customers and find that 11 would pay $100 for the upgrade.
(a) If the upgrade is to be profitable, you will need to sell it to more than 20% of your customers.
Do the sample data give good evidence that more than 20% are willing to buy?
(b) Find a 95% confidence interval for the proportion of all of your customers who would be
willing to buy the upgrade for $100.
Chapter 12
8
Practice Test 12