3-12 e) What percent of the shoppers with only high school

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Statistics Chapter 3: Smoking and Education - KEY
200 adults shopping at a supermarket were asked about the highest level of education they had
completed and whether or not they smoke cigarettes. Results are summarized in the table
High school
2 yr college
4+ yr college
Total
1.
Smoker
32
5
13
50
Non-smoker
61
17
72
150
Total
93
22
85
200
Discuss the W’s.
Who: 200 adults. What: education level and smoking habits When: not specified
Where: shopping mall How: not specified. Was this a random sample, or were some people simply asked?
Why: to examine possible links between smoking and education level
2.
Identify the variables.
Categorical variables: Education level, and whether or not the person was a smoker.
3.
Find each percent requested below.
d) What percent of the shoppers were smokers with only high school
educations?
e) What percent of the shoppers with only high school educations were
smokers?
f) What percent of the smokers had only high school educations?
4.
32
200
32
93
= 16%
≈ 34.4%
32
50
= 64%
Do these data suggest there is an association between smoking and education level? Give
statistical evidence to support your conclusion.
These data provide evidence of an association between smoking and education level. 64% of smokers had
only a high school diploma, while only 40.7% of non-smoker had only high school diplomas. Only 26% of
smokers had four or more years of college, compared to 48% of smokers.
5.
Follow-up question: Does this indicate that students who start smoking while in high school
tend to give up the habit if they complete college? Explain.
These data do not indicate that students who start smoking in high school tend to give up the habit if they
complete college. These data were gathered at one time, about two different groups, smokers and nonsmokers. We have no idea if smoking behavior changes over time.
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley.
3-12
7.
Why do the column totals equal 100%, but the row totals do not?
Major
Major
1.
2.
3.
4.
5.
6.
Statistics Chapter 3: Review A – KEY
Birth Order
1
2
3 4+ Total
34 14 6
3
57
Math/Science
52 27 5
9
93
Agriculture
15 17 8
3
43
Humanities
12 11 1
6
30
Other
113 69 20 21
223
Total
What percent of these students are oldest or only children? 113/223 = 51%
What percent of the Humanities majors are oldest children? 15/43 = 35%
What percent of oldest children are Humanities students? 15/113 = 13%
What percent of the students are oldest children majoring in the Humanities? 15/223 = 7%
Find the marginal distribution of majors. 26% Math/Sci, 42% Ag, 19% Humanities, 13% Other
Complete this table showing the conditional relative distribution of majors for each birth
order.
Birth Order
1
2
3
4+
20%
14%
30%
30%
Math/Science
46%
39%
25% 43%
Agriculture
25%
13%
40% 14%
Humanities
29%
11%
16%
5%
Other
100% 100% 100% 100%
Total
We are finding the conditional distribution of major within each birth order, not the other way around.
8.
Do you think choice of major is independent of birth order? Use statistics to justify your
reasoning.
No, there appears to be an association between major and birth order. The conditional distributions of major
by birth order are different.
9.
Examine the pie graphs below and explain how they provide evidence to support or refute
your answer to question 8.
The pie charts provide support to the association between major and birth order. The pie charts show a
different distribution of major for each birth order. If major and birth order were independent, we would
expect each pie chart to show a similar distribution.
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley.
3-14
Statistics Chapter 3: Review B – KEY
Age
The Pew Research Center conducts surveys regularly asking respondents which political party they
identify with. Among their results is the following table relating prefer political party and age
(http://people-press.org/reports/)
Party
Republican
Democrat
Others Total
2636
2738
4765 10139
18-29
6871
6442
8160 21473
30-49
3896
4286
4806 12988
50-64
3131
3718
2934
9784
65+
16535
17183
20666 54384
Total
1.
Identify the variables, tell their possible values, and identify each variable as categorical or
quantitative.
Party – Categorical variable with values Republican, Democrat, Other
Age – Categorical variable with values 18 – 29, 30 – 49, 50 – 64, and 65+.
2.
Identify the W’s of this study. Which W’s are unknown?
Who – Not specified (probably US residents) What – Party and age range.
Where – Not specified (Probably US) When – Not specified. Why – Opinion polling
How – Survey.
3.
What percent of people surveyed were Republicans? 16535/54384 = 30.4%
4.
What percent of people surveyed were under 30 or over 65? (10139+3131)/54384 = 24.4%
5.
What percent of the people classified as “Other” were under 30? 4765/20666 = 23.1%
6.
What percent of the people under 30 were classified as “Other”? 4765/10139 = 47.0%
7.
What is the marginal distribution of ages?
18.6% of the respondents were 18 – 29 years old, 39.5% were 30 – 49, 23.9% were 50 – 64 and 18.0% were
over 65 years old.
8.
Find the conditional relative frequency of ages among democrats.
15.9% of the Democrats were 18 – 29 years old, 37.5% were 30 – 49, 24.9% were 50 – 64 and 21.6% were
over 65 years old.
9.
Do you think party affiliation is independent of age? Give statistical evidence to support your
conclusion.
There is some evidence of an association between party affiliation and age. Although the conditional
distributions of age (from youngest to oldest) for the Democrats (15.9%, 37.5%, 24.9%, 21.6%) and
Republicans (15.9%, 41.6%, 23.6%, 18.9%) were similar, the conditional distribution of age for the Other
category (23.1%, 39.5%, 23.3%, 14.2%) showed a slightly higher percentage of younger respondents and a
slightly lower percentage of older respondents than the two main political parties.
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley.
3-16
Statistics Chapter 3: Review C – KEY
Bus
Ride
Personal
Total
Male
30
37
19
86
Female
34
45
23
102
Total
64
82
42
188
In order to plan transportation and parking needs at a private high school, administrators asked
students how they get to school. Some rode a school bus, some rode in with parents or friends, and
others used “personal” transportation – bikes, skateboards, or just walked. The table summarizes
the responses from boys and girls.
1.
Identify the variables and tell whether each is categorical or quantitative.
Gender and mode of transportation, both categorical.
2.
Which of the W’s are unknown for these data?
We don’t know how or when the students were surveyed, nor where the school is.
3.
4.
Find each percent.
a. What percent of the students are girls who ride the bus?
b. What percent of the girls ride the bus?
c. What percent of the bus riders are girls?
18.1%
33.3%
53.1%
Identify the marginal distribution of gender.
There are 86 males and 102 females
5.
Write a sentence or two about the conditional relative frequency distribution of modes of
transportation for the boys.
More boys (43%) caught rides to school than any other means of transportation. 35% rode the bus while only
22% used personal transportation like biking, skateboarding, or walking.
6.
Do you think mode of transportation is independent of gender? Give statistical evidence to
support your conclusion.
The way students get to school does seem to be independent of gender. Overall, 34% of students ride the bus,
compared to 35% of the boys and 33% of the girls. 44% of all students caught rides with someone and 22%
used personal transportation, almost the same as the percentages for boys (43% and 22%) or girls (44% and
23%) separately. These data provide little indication of a difference in mode of transportation between boys
and girls at this school
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley.
3-18
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