AP Statistics FR Practice #2
1. As a part of the United States Department of Agriculture’s Super Dump cleanup efforts in the early
1990s, various sites in the country were targeted for cleanup. Three of the targeted sites—River X, River
Y, and River Z—had become contaminated with pesticides because they were located near abandoned
pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide) were
taken at twenty randomly selected locations in each river near the dump sites.
The boxplots shown below display the five-number summaries for the concentrations, in parts per million
(ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers.
(a) Compare the distributions of the concentration of aldrin among the three rivers.
(b) The twenty concentrations of aldrin for River X are given below.
3.4
4.0
5.6
3.7
8.0
5.5
5.3
4.2
4.3
8.6
5.1
8.7
4.6
7.5
5.3
8.2
4.7
4.8
Construct a stemplot that displays the concentrations of aldrin for River X.
7.3
4.6
(c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in the
stemplot but cannot be seen in the boxplot.
2. An advertising agency in a large city is conducting a survey of adults to investigate whether there is an
association between highest level of educational achievement and primary source for news. The company
takes a random sample of 2,500 adults in the city. The results are shown in the table below.
HIGHEST LEVEL OF EDUCATIONAL ACHIEVEMENT
Primary Source
for News
Newspapers
Local television
Cable television
Internet
None
Total
Not High School
Graduate
49
90
113
41
77
370
High School
Graduate But Not
College Graduate
205
170
496
401
165
1,437
College Graduate
188
75
147
245
38
693
Total
442
335
756
687
280
2,500
(a) If an adult is to be selected at random from this sample, what is the probability that the selected
adult is a college graduate or obtains news primarily from the internet?
(b) If an adult who is a college graduate is to be selected at random from this sample, what is the
probability that the selected adult obtains news primarily from the internet?
(c) When selecting an adult at random from the sample of 2,500 adults, are the events “is a college
graduate” and “obtains news primarily from the internet” independent? Justify your answer.
(d) The company wants to conduct a statistical test to investigate whether there is an association
between educational achievement and primary source for news for adults in the city. What is the
name of the statistical test that should be used?
What are the appropriate degrees of freedom for this test?
3. A recent report stated that less than 35 percent of the adult residents in a certain city will be able to pass
a physical fitness test. Consequently, the city’s Recreation Department is trying to convince the City
Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical
of the report. The council will fund more physical fitness programs only if the Recreation Department can
provide convincing evidence that the report is true.
The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of
significance will be conducted at a significance level of α= 0.05 for the following hypotheses.
H0: p = 0.35
Ha: = < 0.35,
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
(a) Describe what a Type II error would be in the context of the study, and also describe a consequence of
making this type of error.
(b) The Recreation Department recruits 185 adult residents who volunteer to take the physical fitness test.
The test is passed by 77 of the 185 volunteers, resulting in a p-value of 0.97 for the hypotheses stated
above. If it was reasonable to conduct a test of significance for the hypotheses stated above using the
data collected from the 185 volunteers, what would the p-value of 0.97 lead you to conclude?
(c) Describe the primary flaw in the study described in part (b), and explain why it is a concern.