Download AP Statistics Practice Test

AP Statistics Practice Test
Unit Eleven – Inference for Categorical Data
Name______________________________________Period________Date________________
Vocabulary:
1.
Name the three different types of Chi-square tests and how they differ from each other.
2.
Briefly describe the Chi-square distribution by listing five major characteristics of this distribution.
3.
Briefly explain what the  test statistic measures.
4.
Fifty tosses of a dime yield 28 heads. For testing the fairness of the coin,
2
2
H o : pH  .5, pT  .5, the value of
is: _____________________
At the 0.05 significance level would you reject or fail to reject H o?
______________________
Why?
5.
A random sample of students from a particular university will be selected and each will be classified by their
university campus (there are six campuses) and as liberal, moderate or conservative with respect to political
philosophy. The hypothesis of interest is that campus and political philosophy are independent factors.
a.
On how many degrees of freedom will the resulting Chi-square test be based?
_____________________________
b.
If 
2
 24.65 , what is the corresponding P-value according to the Chi-square Table?
_____________________________
1
Multiple Choice:
6.
A two-way table of counts is analyzed to examine the hypothesis that the row and column classifications are
independent. There are 3 rows and 4 columns. The degrees of freedom for the chi-square statistic are
(a) 11
(b) 12
(c) 8
(d) 6
(e) The minimum of n1  1 and n2  1
The next four questions refer to the following situation – Use the Chi-square Table – A study was
conducted to determine if the fatality rate depends on the size of the automobile. The analysis of accidents is as
follows (with some values hidden):
FATALITY
SIZE
FREQUENCY|
m
|
s
|
l
|
---------+--------+--------+--------+
no
|
63 |
128 |
46 |
---------+--------+--------+--------+
yes
|
26 |
95 |
16 |
---------+--------+--------+--------+
TOTAL
89
223
62
TOTAL
237
137
374
STATISTICS FOR TABLE OF DEATH BY SIZE
STATISTIC
DF
VALUE
PROB
-----------------------------------------------------CHI-SQUARE
*
8.663
*****
7. The expected frequency for the cell corresponding to fatal type of accident and small size automobile is:
(a) 81.69
(b) 67.00
Find the expected value for this cell using the formula.
(c) 141.31
SHOW YOUR WORK HERE FOR CREDIT:
(d) 63.41
(e) 95.72
8. Which of the following is NOT CORRECT?
(a) The accidents were cross classified by size of automobile and fatality status. Each accident was counted
in one and only one cell.
(b) One null hypothesis is that the fatality status is independent of the size of the automobile.
(c) One alternative hypothesis is that there is an association between fatality status and size of automobile.
(d) If all expected cell counts are greater than five, then the distribution of the test statistic is an approximate
chi-square distribution.
(e) If we reject the null hypothesis then we have proven that the size of the automobile causes the fatality.
9. The null hypothesis will be rejected at
(a) 12.59
(b) 7.81
(c) 5.99
(d) 3.84
(e) 9.49
  0.05 if the test statistic exceeds:
10. The approximate P-value is:
(a) between 0.020 and 0.0250
(b) between 0.005 and 0.010
(c) between 0.010 and 0.020
(d) between 0.025 and 0.050
(e) between 0.050 and 0.100
2
Free Response:
11. Last season, at the 8:00 p.m. time slot, television channels 3, 5, 8 and 13 captured the entire audience with
30%, 25%, 20% and 25% of the viewers, respectively. During the first week of the next season, 500
randomly chosen viewers are interviewed. Suppose that the actual numbers during the same time slot are as
follows:
Channel
3
Frequency 139
5
138
8
112
13
111
Carry out an appropriate test to determine if this distribution of viewers is significantly different than the
previous season. Use a significance level of 0.05. Make sure to include all the necessary steps.
12. The nonprofit group Public Agenda conducted telephone interviews with three randomly selected groups of
parents of high-school children. There were 202 black parents, 202 Hispanic parents, and 201 white parents.
The sample survey asked the parents to respond to the statement, “A college education has become as
important as a high school diploma used to be." Here are the counts of responses:
Do you believe that there are differences between the groups? Do the appropriate statistical test at the 0.01
level.
3
13. A medical researcher tests 640 heart attack victims for the presence of a certain antibody in their blood and
cross-classifies against the severity of the attack. The results are reported in the following table:
Severity of the Attack
Antibody
Present
Positive Test
Negative Test
Severe
85
40
Medium
125
95
Mild
150
145
Is there evidence of an association between presence of the antibody and severity of the heart attack? Let
  0.05 .
14. A study of accident records at a large engineering company in England reported the following number of
injuries on each shift for 1 year:
Shift:
Number of injuries:
Morning
1332
Afternoon
1598
Night
1706
Is there sufficient evidence to say that the numbers of accidents on the three shifts are not the same? Test at
the 0.01 level.
14b. Which component was the largest contributor to the
4
2
test statistic and in what direction?
Review:
15. Acme Corporation manufactures light bulbs. The CEO claims that an average Acme light bulb lasts 300 days.
A researcher randomly selects 15 bulbs for testing. The sampled bulbs last an average of 290 days, with a
standard deviation of 50 days. If the CEO's claim were true, what is the probability that 15 randomly selected
bulbs would have an average life of no more than 290 days?
a)
b)
c)
d)
e)
0.100
0.226
0.334
0.443
0.775
16. Bob is a high school basketball player. He is a 70% free throw shooter. That means his probability of making
a free throw is 0.70. What is the probability that Bob makes his first free throw on his fifth shot?
a)
b)
c)
d)
e)
0.0024
0.0057
0.0081
0.0720
0.1681
17. A national consumer magazine reported the following correlations.
 The correlation between car weight and car reliability is -0.30.
 The correlation between car weight and annual maintenance cost is 0.20.
Which of the following statements are true?
I. Heavier cars tend to be less reliable.
II. Heavier cars tend to cost more to maintain.
III. Car weight is related more strongly to reliability than to maintenance cost.
a)
b)
c)
d)
e)
I only
II only
III only
I and II
I, II, and III
18. With respect to experimental design, which of the following statements are true?
I. Blinding controls for the effects of confounding.
II. Randomization controls for effects of lurking variables.
III. Each experimental factor has one treatment level.
a)
b)
c)
d)
e)
I only
II only
III only
All of the above.
None of the above.
19. Suppose X and Y are independent random variables. The variance of X is equal to 16 and the variance of Y
is equal to 9. Let Z = X – Y. What is the standard deviation of Z?
a)
b)
c)
d)
2.65
5.00
7.00
25.0
e) It is not possible to answer this question, based on the information given.
5