Deck 3: Relationships Between Categorical Variablescontingency Tables

Question 1

A company interested in the health of its employees started a health program including
Monitoring blood pressure.Based on age, employees were categorized according to ranges of Blood pressure by age intervals.Data are shown in the table below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Age }$ $\begin{array} { | c | c | c | c | c | } \hline \text { BP } & \text { Under 30 } & \mathbf { 3 0 } - \mathbf { 4 9 } & \text { Over } \mathbf { 5 0 } & \text { Total } \\\hline \text { Low } & 27 & 38 & 31 & 96 \\\hline \text { Normal } & 48 & 90 & 92 & 230 \\\hline \text { High } & 23 & 59 & 72 & 154 \\\hline \text { Total } & 98 & 187 & 195 & 480 \\\hline\end{array}$

Of all employees, the percentage of those under 50 years old is

A)17.1% (82/480).
B)40.6% (195/480).
C)13.5% (65/480).
D)36.9% (72/195).
E)49.4% (285/480).

Answer 1

49.4% (285/480).

Question 2

A company interested in the health of its employees started a health program including
Monitoring blood pressure.Based on age, employees were categorized according to ranges of
Blood pressure by age intervals.Data are shown in the table below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Age }$
$\begin{array} { | c | c | c | c | c | } \hline \text { BP } & \text { Under 30 } & \mathbf { 3 0 } - \mathbf { 4 9 } & \text { Over 50 } & \text { Total } \\\hline \text { Low } & 27 & 38 & 31 & 96 \\\hline \text { Normal } & 48 & 90 & 92 & 230 \\\hline \text { High } & 23 & 59 & 72 & 154 \\\hline \text { Total } & 98 & 187 & 195 & 480 \\\hline\end{array}$
The percentage of employees who are over age 50 and have high blood pressure is

A)46.8% (72/154).
B)32.1% (154/480).
C)31.6% (59/187).
D)36.9% (72/195).

Answer 2

36.9% (72/195).

Question 3

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.
Do you think the breed selection is independent of gender? Give statistical evidence to
support your conclusion.

Answer 3

The breed selection does not appear to be independent of gender.Overall, 56% of the respondents were females,
but females were over-represented among those who favored Golden Retrievers (64%) and Dalmatians (62%),
yet a much lower percentage (47%) among those who chose Labradors.

Question 4

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.

-Which of the W's are unknown for these data?

Question 5

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.

-Write a sentence or two about the conditional relative frequency distribution of the breeds
among female respondents.

Question 6

Here is a stacked bar chart for data collected about employee blood pressure. This chart shows

A)the distribution of a quantitative variable.
B)the contingency distribution of blood pressure type.
C)the conditional distribution of blood pressure type.
D)the marginal distribution of blood pressure type.
E)the joint distribution of blood pressure type.

Question 7

A large national retailer of electronics conducted a survey to determine consumer preferences
For various brands of digital cameras and the data are summarized in the table shown below. $$\begin{array} { | c | c | c | c | } \hline & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Cannon Power Shot } & 73 & 59 & \mathbf { 1 3 2 } \\\hline \text { Nikon Cool Pix } & 49 & 47 & \mathbf { 9 6 } \\\hline \text { Sony Cyber Shot } & 58 & 33 & \mathbf { 9 1 } \\\hline \text { Panasonic Lumix } & 35 & 30 & \mathbf { 6 5 } \\\hline \text { Fujifilm Finepix } & 45 & 28 & \mathbf { 7 3 } \\\hline \text { Olympus S/V } & 37 & 41 & \mathbf { 7 8 } \\\hline \text { Other Brands } & 86 & 67 & \mathbf { 1 5 3 } \\\hline \text { Total } & \mathbf { 3 8 3 } & \mathbf { 3 0 5 } & \mathbf { 6 8 8 } \\\hline\end{array}$$
The percentage of consumers who are male and prefer Fujifilm is

A)44.3 % (305/688).
B)10.6% (73/688).
C)38.4% (28/73).
D)56.2% (41/73).
E)4.1% (28/688).

Question 8

The following is a bar chart summarizing consumer preferences for various brands of digital
Cameras.
This bar chart shows

A)the marginal distribution of brands.
B)the conditional distribution of brands.
C)the contingency distribution of brands.
D)the distribution for a quantitative variable.
E)none of the above.

Question 9

A large national retailer of electronics conducted a survey to determine consumer preferences
For various brands of digital cameras and the data are summarized in the table shown below.
Of the consumers who prefer Olympus, what percentage is female? $$\begin{array} { | c | c | c | c | } \hline & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Cannon Power Shot } & 73 & 59 & \mathbf { 1 3 2 } \\\hline \text { Nikon Cool Pix } & 49 & 47 & \mathbf { 9 6 } \\\hline \text { Sony Cyber Shot } & 58 & 33 & \mathbf { 9 1 } \\\hline \text { Panasonic Lumix } & 35 & 30 & \mathbf { 6 5 } \\\hline \text { Fujifilm Finepix } & 45 & 28 & \mathbf { 7 3 } \\\hline \text { Olympus S/V } & 37 & 41 & \mathbf { 7 8 } \\\hline \text { Other Brands } & 86 & 67 & \mathbf { 1 5 3 } \\\hline \text { Total } & \mathbf { 3 8 3 } & \mathbf { 3 0 5 } & \mathbf { 6 8 8 } \\\hline\end{array}$$

A)47.4 % (37/78).
B)6.0% (41/688).
C)52.6% (41/78).
D)11.7% (45/383).
E)11.3% (78/688).

Question 10

A company interested in the health of its employees started a health program including
Monitoring blood pressure.Based on age, employees were categorized according to ranges of
Blood pressure by age intervals.Data are shown in the table below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Age }$ $\begin{array} { | c | c | c | c | c | } \hline \text { BP } & \text { Under 30 } & \mathbf { 3 0 } - \mathbf { 4 9 } & \text { Over } \mathbf { 5 0 } & \text { Total } \\\hline \text { Low } & 27 & 38 & 31 & 96 \\\hline \text { Normal } & 48 & 90 & 92 & 230 \\\hline \text { High } & 23 & 59 & 72 & 154 \\\hline \text { Total } & 98 & 187 & 195 & 480 \\\hline\end{array}$
Of all employees, the percentage who are over 50 and have high blood pressure is

A)46.8% (72/154).
B)15.0% (72/480).
C)31.6% (59/187).
D)36.9% (72/195).
E)47.2% (92/195).

Question 11

In May, 2010, the Pew Research Center for the People & the Press carried out a national
Survey to gauge opinion on the Arizona Immigration Law.Responses (Favor, Oppose, Don't
Know) were examined according to groups defined by political party affiliation (Democrat,
Republican, Independent).Which of the following would be appropriate for displaying these
Data?

A)Contingency table.
B)Pie charts.
C)Segmented bar chart.
D)Side by side bar chart.
E)All of the above.

Question 12

A company interested in the health of its employees started a health program including
Monitoring blood pressure.Based on age, employees were categorized according to ranges of
Blood pressure by age intervals.Data are shown in the table below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Age }$ $\begin{array} { | c | c | c | c | c | } \hline \text { BP } & \text { Under 30 } & \mathbf { 3 0 } - \mathbf { 4 9 } & \text { Over } \mathbf { 5 0 } & \text { Total } \\\hline \text { Low } & 27 & 38 & 31 & 96 \\\hline \text { Normal } & 48 & 90 & 92 & 230 \\\hline \text { High } & 23 & 59 & 72 & 154 \\\hline \text { Total } & 98 & 187 & 195 & 480 \\\hline\end{array}$

The percentage of employees with normal or low blood pressure is

A)67.9% (326/480).
B)47.9% (230/480).
C)41.7% (96/230).
D)80.0% (384/480).
E)20.0% (96/480).

Question 13

What is the marginal distribution of milk consumption?

Question 14

Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (Shanthy A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239):




-Consider the following pie charts of a subset of the data above:


Do the pie charts above indicate that milk consumption by young girls is independent of the
nationwide survey year? Explain.

Question 15

A large national retailer of electronics conducted a survey to determine consumer preferences
For various brands of digital cameras and the data are summarized in the table shown below. $$\begin{array} { | c | c | c | c | } \hline & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Cannon Power Shot } & 73 & 59 & \mathbf { 1 3 2 } \\\hline \text { Nikon Cool Pix } & 49 & 47 & \mathbf { 9 6 } \\\hline \text { Sony Cyber Shot } & 58 & 33 & \mathbf { 9 1 } \\\hline \text { Panasonic Lumix } & 35 & 30 & \mathbf { 6 5 } \\\hline \text { Fujifilm Finepix } & 45 & 28 & \mathbf { 7 3 } \\\hline \text { Olympus S/V } & 37 & 41 & \mathbf { 7 8 } \\\hline \text { Other Brands } & 86 & 67 & \mathbf { 1 5 3 } \\\hline \text { Total } & \mathbf { 3 8 3 } & \mathbf { 3 0 5 } & \mathbf { 6 8 8 } \\\hline\end{array}$$
Of the consumers who are male, the percentage who prefer Sony is

A)44.3 % (305/688).
B)10.8% (33/305).
C)36.3% (33/91).
D)4.8% (33/688).

Question 16

Do you think that milk consumption by young girls is independent of the nationwide survey
year? Use statistics to justify your reasoning.

Question 17

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.

-Find each percent.
a. What percent of the responses were from males who favor Labradors?______
b. What percent of the male responses favor Labradors?__________
c. What percent of the people who choose Labradors were males?_________

Question 18

Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (Shanthy A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239):




-a. What percent of the young girls reported that they drink milk? ______
b. What percent of the young girls were in the 1989-1991 survey?_______
c. What percent of the young girls who reported that they drink milk were in the 1989-1991 survey?_____
d. What percent of the young girls in 1989-1991 reported they drink milk?_______

Question 19

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.

-Identify the variables and tell whether each is categorical or quantitative.
$$\begin{array} { | c | c | c | c | } \hline & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Yorkshire Terrier } & 73 & 59 & \mathbf { 1 3 2 } \\\hline \text { Dachshund } & 49 & 47 & \mathbf { 9 6 } \\\hline \text { Golden Retriever } & 58 & 33 & \mathbf { 9 1 } \\\hline \text { Labrador } & 37 & 41 & \mathbf { 7 8 } \\\hline \text { Dalmatian } & 45 & 28 & \mathbf { 7 3 } \\\hline \text { Other breeds } & 86 & 67 & \mathbf { 1 5 3 } \\\hline \text { Total } & \mathbf { 3 4 8 } & \mathbf { 2 7 5 } & \mathbf { 6 2 3 } \\\hline \end{array}$$

Question 20

To determine if people's preference in dogs had changed in the recent years, organizers of a local
dog show asked people who attended the show to indicate which breed was their favorite. This
information was compiled by dog breed and gender of the people who responded. The table
summarizes the responses.

-What is the marginal distribution of breeds?

Question 21

Accenture, a consulting firm, conducted an online survey of 500 US consumers from in 2013. What percentage of men were felt that better discounts were available on "Black Friday"?

A)26.5%
B)65%
C)20%
D)17.8%
E)5.5%

Question 22

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law.The results are displayed in the segmented bar chart below.Which of the
Following statements is true?

A)A greater percentage of Republicans oppose the law compared to Democrats.
B)A greater percentage of Republicans oppose the law compared to Independents.
C)Opinion about the law appears to be independent of political party affiliation.
D)A greater percentage of Democrats oppose the law compared to Republicans.
E)The segmented bar chart is not appropriate for these data.

Question 23

Accenture, a consulting firm, conducted an online survey of 500 US consumers from in 2013. What percentage of those who thought that better discounts were available on "Black Friday"
Were female?

A)81.3%
B)33.3%
C)11.1%
D)47.2%
E)23.5%

Question 24

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law (results shown below).How many respondents are Republican and favor
The law?

A)93
B)45
C)145
D)7

Question 25

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law.Based on the results displayed in the table below, what percent of
Respondents is Independent?
$$\begin{array} { | l | l | l | l | } \hline \text { Response } & \text { Democrat } & \text { Republican } & \text { Independent } \\\hline \text { Favor } & 50 & 93 & 35 \\\hline \text { Oppose } & 85 & 45 & 60 \\\hline \text { Don't Know } & 5 & 7 & 20 \\\hline\end{array}$$

A)35%
B)9%
C)29%
D)45%
E)25%

Question 26

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law (results shown below).Of respondents who are Democrat, what percent
Oppose the law?

A)13%
B)35%
C)22%
D)45%
E)61%

Question 27

Accenture, a consulting firm, conducted an online survey of 500 US consumers in September 2013.Based on their response to the question "What is your motive for shopping late in the
Season?" which of the following would be appropriate method(s) for displaying the male
Only data shown in the table?

A)Contingency table.
B)Pie chart.
C)Segmented bar chart.
D)Side by side bar chart.
E)All of the above.

Question 28

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law (results shown below).What percent oppose the law?

A)48%
B)45%
C)32%
D)25%
E)61%

Question 29

A regional survey was carried out to gauge public opinion on the controversial Arizona
Immigration Law (results shown below).Of respondents who oppose the law, what percent
Is Democrat?
$$\begin{array} { | l | l | l | l | } \hline \text { Response } & \text { Democrat } & \text { Republican } & \text { Independent } \\\hline \text { Favor } & 50 & 93 & 35 \\\hline \text { Oppose } & 85 & 45 & 60 \\\hline \text { Don't Know } & 5 & 7 & 20 \\\hline\end{array}$$

A)13%
B)35%
C)22%
D)45%