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Practice Test 14
AP Statistics
Name:
Directions: Work on these sheets.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. A chi-square goodness of fit test is used to test whether a 0 to9 spinner is “fair” (that is, the
outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded.
Which member of the chi-square family of curves is used?
2
2
2
2
(a)  (8)
(b)  (9)
(c)  (10)
(d)  (99)
(e) None of the above
2. 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
1372
Afternoon
1578
Night
1686
Is there sufficient evidence to say that the numbers of accidents on the three shifts are not the
same? Test at the 0.05, 0.01, and 0.001 levels.
(a) There is sufficient evidence at all three levels to say that the numbers of accidents on each shift
are not the same.
(b) There is sufficient evidence at the 0.05 and 0.01 levels but not at the 0.001 level.
(c) There is sufficient evidence at the 0.05 level but not at the 0.01 or 0.001 levels.
(d) There is sufficient evidence at the 0.001 level but not at the 0.01 or 0.05 levels.
(e) There is insufficient evidence at any of these levels.
Questions 3 to 10 refer to the following situation.
In the paper “Color Association of Male and Female Fourth-Grade School Children” (Journal of
Psychology, 1988, 383–388), reported on a study in which children were asked to indicate what
emotion they associated with the color red. The response and the sex of the child are noted and
summarized below. The first number in each cell is the count; the second number is the row percent.
Female
Male
Total
Statistic
Pearson Chi-Square
Likelihood Ratio Chi-Square
Mantel-Haenszel Chi-Square
Anger
27
26.47
34
30.36
61
Happy
19
18.63
12
10.71
31
DF
*
*
1
Love
39
38.24
38
33.93
77
Pain
17
16.67
28
25.00
45
Value
4.629
4.661
0.307
Total
102
112
214
Prob
*****
*****
*****
3. The null hypothesis is
(a) emotional association with red is independent of gender.
(b) gender is dependent upon the emotional association with red.
(c) the probability of associating a specific emotion with red is related to gender.
(d) the number of children in each cell does not depend upon gender or upon emotion.
(e) the color red is independent of the emotion associated with it and with gender.
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4. Under a suitable null hypothesis, the expected frequency for the cell corresponding to Anger and
Males is
(a) 15.9.
(b) 55.7.
(c) 30.4.
(d) 31.9.
(e) 29.1.
5. The null hypothesis will be rejected at  = 0.05 if the test statistic exceeds
(a) 3.84.
(b) 5.99.
(c) 7.81.
(d) 9.49.
(e) 14.07.
6. The approximate P-value is
(a) between 0.100 and 0.900.
(b) between 0.050 and 0.100.
(c) between 0.025 and 0.050.
(d) between 0.010 and 0.025.
(e) between 0.005 and 0.010.
7. Which of the following is NOT CORRECT?
(a) The children were classified by sex and emotion associated with red. Each child was counted in
one and only one cell.
(b) The null hypothesis is that the type of emotion associated with red is independent of the sex of
the child.
(c) The null hypothesis is that the proportion of emotions associated with red is the same for both
sexes.
(d) All expected cell counts should be greater than 5 in order that 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 two sexes associate red with
emotions in different ways.
8. Which of the following is NOT CORRECT?
(a) A lower percent of female students associate the emotion “anger” with the color red than do
male students.
(b) More students associate the color red with the emotion “love” than with the emotion “anger.”
(c) There is insufficient evidence of an association between gender and emotion associated with the
color red.
(d) We will be unable to compute a correlation for these data because the variables are both
categorical.
(e) We compute row or column percents by dividing the cell count by the table total (214).
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9. A Type I error would be committed if
(a) we conclude that the sex of the child and the emotion associated with red are independent when
in fact they are not independent.
(b) we conclude that the sex of the child and the emotion associated with red are not independent
when in fact they are not independent.
(c) we conclude that the proportion of emotions associated with red differs between males and
females when in fact they are the same.
(d) we conclude that the proportion of emotions associated with red is the same for males and
females when in fact they are the same.
(e) we fail to find any association between the color red and emotions for either sex.
10. The test statistic and approximate P-value are
(a) 4.661 0.1983
(b) 4.661 0.3966
(c) 4.629 0.2011
(d) 4.629 0.4022
(e) 4.629 0.1006
Questions 11 to 13 relate to the following situation.
A sample of 102 drug users was interviewed and each subject was asked to name the kind of drug that
each first injected. Here are the results:
First drug injected
Heroin
Speed
Other
Number
42
36
24
11. An appropriate null hypothesis is
(a) the count of first drug injected is the same for each drug category.
(b) µ = 34.
(c) at least one of the cell counts is different from the other two.
(d) the proportion of first drug injected depends on the type of drug.
(e) the 3 cell counts are independent of the type of drug.
12. The test statistic, degrees of freedom, and P-value are
(a) 4.94, 2, 0.0845.
(b) 1.88, 2, 0.391.
(c) 2.94, 3, 0.40.
(d) 0.118, 2, 0.94.
(e) 8.94, 2, 0.011.
13. Which of the following is a correct statement? In order to make an inference about the population,
(a) the population has to be at least 10 times the size of the sample.
(b) the cell counts for our sample have to be approximately the same as the counts for the host
population.
(c) all observed cell counts have to be positive, and no more than 20% can be less than 15.
(d) the sample has to have the same characteristics as the population.
(e) the subjects have to be a random sample of drug users.
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14. Are all employees equally prone to having accidents? To investigate this hypothesis, a researcher
looked at a light manufacturing plant and classified the accidents by type and by age of the
employee.
Age
Under 25
25 or over
Sprain
| 9
| 61
Accident Type
Burn
17
13
Cut
5
12
A chi-square test gave a test statistic of 20.78. If we test at  = 0.05
(a) there appears to be no association between accident type and age.
(b) age seems to be independent of accident type.
(c) accident type does not seem to be independent of age.
(d) there appears to be a 20.78% correlation between accident type and age.
(e) the proportion of sprain, cuts, and burns seems to be similar for both age classes.
15. Each person in a random sample of 50 was asked to state his/her sex and preferred color. The
resulting frequencies are shown below.
Male
Female
Red
5
15
Color
Blue Green
14
6
6
4
A chi-square test is used to test the null hypothesis that sex and preferred color are independent.
Which of the following statements is a correct decision about the null hypothesis?
(a) Reject at the 0.005 level.
(b) Reject at the 0.01 level but not at the 0.005 level.
(c) Reject at the 0.025 level but not at the 0.01 level.
(d) Reject at the 0.05 level but not at the 0.025 level.
(e) Accept at the 0.05 level.
16. The following data were obtained from a company that manufactures special plastic containers that
are to hold a specified volume of hazardous material. On each of the three 8-hour shifts workers are
able to make 500 of the containers. Some containers do not meet specifications as required by the
company’s customer because they are too small; others, because they are too large.
Shift
8 am
4 pm
Midnight
Too small
36
24
12
Conformance to Specification
Within spec.
Too large
452
12
443
33
438
50
If conformance to specifications is independent of shift, the expected number of containers that
meet specifications on the 4 pm shift is
(a) 166.7.
(b) 443.
(c) 33.
(d) 444.3.
(e) 500.
17. A survey was conducted to investigate whether alcohol consumption and smoking are related. The
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following information was compiled for 600 individuals:
Smoker
193
89
Drinker
Nondrinker
Nonsmoker
165
153
Which of the following statements is true?
(a) The appropriate alternative hypothesis is Ha: Smoking and alcohol consumption are
independent.
(b) The appropriate null hypothesis is H0: Smoking and alcohol consumption are not independent.
(c) The calculated value of the test statistic is 3.84.
(d) The calculated value of the test statistic is 7.86.
(e) At level 0.01 we conclude that smoking and alcohol consumption are related.
18. A controversial issue in sports is the use of the “instant replay” for making decisions on plays that
are extremely close or hard to call by an official. A random survey of players in each of four
professional sports was conducted, asking them if they felt instant replays should be used to decide
close or controversial calls. The results are as follows:
Use of Instant Replay
Favor
Oppose
Football
22
2
Baseball
18
6
Basketball
15
26
Soccer
3
10
In testing to see whether opinion with respect to the use of instant replays is independent of sport, a
table of expected frequencies is found. In this table, the expected number of professional baseball
players opposing the use of instant replays is equal to:
(a) 10.4
(b) 24.1
(c) 11.0
(d) 6.0
(e) 8.4
19. In the context of the previous problem, software gives the test statistic as X2 = 28.0 and the P-value
as 0.000. Which of the following statements is correct?
(a) We cannot proceed with inference because two of the entries are less than 5.
(b) The purpose of the study is to see if professional athletes’ opinion of instant replays depends on
which sport they play.
(c) The number of the degrees of freedom is 8 – 1 = 7.
(d) According to the central limit theorem, the sample size is large enough to permit us to use the
Normal distribution.
(e) The small P-value (0.000) tells us that there is evidence of a strong association between
professional sports and opinions of the use of instant replays.
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20. A random sample of 100 members of a union is asked to respond to two questions: Question 1.
Are you happy with your financial situation? Question 2. Do you approve of the federal
government’s economic policies? The responses are:
Question
2
Question
Yes
Yes
22
No
12
Total 34
1
No
48
18
66
Total
70
30
100
To test the null hypothesis that response to Question 1 is independent of response to Question 2 at
5% level, the expected frequency for the cell (Yes, Yes) and the critical value of the associated test
statistic are
(a) 23.8 and 1.96 respectively.
(b) 10.2 and 3.84 respectively.
(c) 23.8 and 3.84 respectively.
(d) 23.8 and 7.81 respectively.
(e) 10.2 and 7.81 respectively.
Part 2: Free Response
Communicate your thinking clearly and completely.
21. An experiment in chicken breeding results in offspring having very curly, slightly curly, or normal
feathers. If this is the result of a single gene system, then the proportions of offspring in the three
phenotypes should be 0.25, 0.50, and 0.25 respectively. In one such experiment, 93 chickens were
born. 20 had normal feathers, 50 had slightly curly feathers, and 23 had very curly feathers. Carry
out a test to determine whether the genetic model seems to hold in this setting.
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22. In a telephone survey of 800 registered voters, the data are classified both by gender of respondent
and by respondent’s opinion on an environmental bond issue.
Men
Women
For
450
160
Bond Issue
Against
150
40
We want to know whether there is good evidence that one’s gender influences whether a person is
for or against the bond issue. Use the chi-square test to answer this question. State the hypotheses,
discuss conditions, perform calculations, and report your conclusions.
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23. Births are not evenly distributed across the days of the week. Fewer babies are born on Saturday
and Sunday than on other days, probably because doctors find weekend births inconvenient. A
random sample of 700 births from local records shows this distribution across the days of the week:
Day
Births
Sun.
84
Mon.
110
Tue.
124
Wed.
104
Thu.
94
Fri.
112
Sat.
72
(a) The null hypothesis is that all days are equally probable. What are the probabilities specified
by this null hypothesis?
(b) What are the expected counts for each day in 700 births?
(c) Calculate the chi-square statistic for goodness of fit.
(d) What are the degrees of freedom for this statistic?
(e) Do 700 births give significant evidence that births are not equally probable on all days of the
week?
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24. A sample survey by the Pew Internet and American Life Project asked a random sample of adults
about use of the Internet and about the type of community they lived in. Here are the results:
Internet users
Nonusers
Rural
433
463
Community Type
Suburban
1072
627
Urban
536
388
Is there a relationship between Internet use and community type? Give statistical evidence to
support your findings.
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