Test 14B
AP Statistics
Name:
Directions: Work on these sheets.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
Questions 1 to 3 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
1. 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.
2. 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.
3. 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.
4. 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.
Chapter 14
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Test 14B
5. 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.
6. 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.
7. A survey was conducted to investigate whether alcohol consumption and smoking are related. The
following information was compiled for 600 individuals:
Drinker
Nondrinker
Smoker
193
89
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.
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Test 14B
Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps.
8. Your school administration wants to install new soft drink machines in the gym and cafeteria.
Their market analysts want to know if flavor preference depends on the location. A random
sample of 180 students was selected and interviewed. Their location and soft drink preference are
given in the table.
Soft drink
Coca-Cola
Pepsi
Sprite
Gym
33
30
5
Cafeteria
57
20
35
(a) Enter the marginal values in the table and the expected counts next to the observed counts.
(b) Write null and alternative hypotheses for a chi-square analysis of these data.
(c) State and verify conditions for carrying out the inference procedure.
(d) Determine the test statistic, the degrees of freedom, and the P-value.
(e) State your conclusion(s).
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Test 14B
9. The M&M/Mars Company reports that their Peanut M&M’s Chocolate Candies are produced in
the following distribution: 20% each of browns, yellows, reds and blues, and 10% each of greens
and oranges. Sam bought a bag of Peanut M&M’s and counted out the following distribution of
colors: 12 brown, 7 yellow, 4 red, 8 blue, 13 green and 2 orange. Perform a goodness of fit test of
the company’s reported distribution and report your results. Do a complete analysis, that is,
include all of the important steps.
I pledge that I have neither given nor received aid on this test.____________________________________________
Chapter 14
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Test 14B
Test 14C
AP Statistics
Name:
Directions: Work on these sheets.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
Questions 1 to 5 relate to the following situation.
A well-known chewing gum maker wants to determine if people who chew gum have a preference of
flavors. A random sample of sales is selected. Here are the results:
Flavor
Number sold
Peppermint
25
Cinnamon
19
Wintergreen
22
Spearmint
14
1. An appropriate null hypothesis for a significance test would be
(a) µ = 20
(b) There is a flavor preference.
(c) The cell counts (above) are independent of flavor.
(d) At least one of the cell counts (above) is different from the other three.
(e) There is no flavor preference.
2. Which of the following are conditions for a chi-square test?
I. There have to be at least 800 gum chewers in the population.
II. If p = proportion of gum chewers, then np ≥ 10 and n(1 – p) ≥ 10.
III. All of the cell counts (above) have to be at least 5.
IV. The sample has to be random.
(a)
(b)
(c)
(d)
(e)
I and III only
II and IV only
IV only
I and IV only
III and IV only
3. The expected counts and degrees of freedom are
(a) 25, 19, 22, 14; 3
(b) 25, 19, 22, 14; 4
(c) 20, 20, 20, 20; 4
(d) 18, 18, 18, 18; 3
(e) 20, 20, 20, 20; 3
4. The test statistic and P-value are
(a) X2 = 3.3; and P = 0.348.
(b) X2 = 0 and P =1.
(c) X2 = 5.2 and P = 0.158.
(d) X2 = 7.7 and P = 0.053.
(e) None of the above is correct.
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Test 14B
5. An appropriate interpretation of this inference procedure is
(a) gum chewers prefer peppermint flavor.
(b) unfortunately, one or more of the conditions for inference is violated, so we can’t conclude
anything from this study.
(c) the P-value is so large that H0 can be rejected. There is no gum preference.
(d) there is insufficient evidence that gum chewers have a preference among these four flavors.
(e) there is sufficient evidence of a gum preference. An additional inference procedure would need
to be done to determine which flavor is preferred.
6. 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
7. 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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Test 14B
8. 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.
9. A recent estimate by a large distributor of gasoline claims that 60% of all cars stopping at their
service stations chose unleaded gas and that super unleaded and regular were each selected 20% of
the time. In order to check the validity of these proportions, a study was conducted of cars
stopping at the distributor’s service stations in a large city. The results were as follows:
Regular
51
Gasoline Selected
Unleaded
Super Unleaded
261
88
Carry out a significance test of the distributor’s claim. Follow the steps in the Inference Toolbox.
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Test 14B
10. A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random
sample of students was selected from schools in Georgia. The students received a questionnaire
regarding achieving personal goals. They were asked what they would most like to do at school:
make good grades, be good at sports, or be popular. Results are presented in the table below by the
sex of the child.
Make good grades
Be popular
Be good at sports
Boys
96
32
94
Girls
295
45
40___
(a) Which type of chi-square procedure is appropriate in this setting? Justify your answer.
(b) Carry out the inference procedure you selected in part (a). Follow the steps in the Inference
Toolbox.
I pledge that I have neither given nor received aid on this test. __________________________________________
Chapter 14
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Test 14B
Test 14D
AP Statistics
Name:
Directions: Work on these sheets. A chi-square table appears at the end of this test.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
Questions 1 through 10 relate to the following setting.
The National Survey of Adolescent Health interviewed several thousand teens (grades 7 to 12). One
question asked was “What do you think are the chances you will be married in the next ten years?”
Here is a two-way table of the responses by sex:
Almost no chance
Some chance, but probably not
A 50-50 chance
A good chance
Almost certain
Female
119
150
447
735
1174
Male
103
171
512
710
756
1. The number of female teenagers in the sample is
(a) 4877.
(b) 2625.
(c) 2252.
(d) 1174.
(e) 756.
2. The percent of the females in the sample who responded “almost certain” is about
(a) 44.7%.
(b) 39.6%.
(c) 33.6%.
(d) 24.1%.
(e) 52.1%.
3. The percent of the females in the sample who responded “almost certain” is
(a) higher than the percent of males who felt this way.
(b) about the same as the percent of males who felt this way.
(c) lower than the percent of males who felt this way.
(d) higher than the percent of males who responded “a good chance” or “almost certain.”
(e) higher than the other categories combined.
4. The expected count of females who respond “almost certain” is about
(a) 464.6.
(b) 891.2.
(c) 777.8.
(d) 891.2.
(e) 1038.8.
Chapter 14
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Test 14B
5. The term in the chi-square statistic for the cell of females who respond “almost certain” is about
(a) 20.5.
(b) 15.6.
(c) 0.1.
(d) 17.6.
(e) 0.13.
6. The degrees of freedom for the chi-square test for this two-way table are
(a) 2.
(b) 4.
(c) 8.
(d) 9.
(e) 20.
7. The null hypothesis for the chi-square test for this two-way table is
(a) Equal proportions of female and male teenagers are almost certain they will be married in ten
years.
(b) There is no difference between female and male teenagers in their opinions about their chances
of being married in ten years.
(c) There are equal numbers of female and male teenagers.
(d) There is a difference between female and male teenagers in their opinions about their chances
of being married in ten years.
(e) There is no association between the number of female teens who responded “almost certain”
and the number of male teens who feel this way.
8. The alternative hypothesis for the chi-square test for this two-way table is
(a) Female and male teenagers do not have the same opinions about their chances of being married
in ten years.
(b) Female teenagers are more likely than male teenagers to think it is almost certain they will be
married in ten years.
(c) Female teenagers are less likely than male teenagers to think it is almost certain they will be
married in ten years.
(d) There is no association between the number of female teens who responded “almost certain”
and the number of male teens who feel this way.
(e) There is an association between the number of female teens who responded “almost certain”
and the number of male teens who feel this way.
9. Software gives the chi-square statistic as X2 = 69.8 for this table. The P-value is
(a) between 0.0025 and 0.001.
(b) between 0.001 and 0.0005.
(c) less than 0.0005.
(d) between 0.005 and 0.001.
(e) between 0.01 and 0.001.
10. The most important fact that allows us to trust the results of the chi-square test is
(a) the sample is large, 4877 teenagers in all.
(b) the sample is close to an SRS of all teenagers.
(c) all of the cell counts are greater than 100.
(d) the P-value is very small.
(e) the X2 test statistic is very large.
Chapter 14
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Test 14B
Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps.
11. 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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Test 14B
12. 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.
I pledge that I have neither given nor received aid on this test.__________________________________________
Chapter 14
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Test 14B