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Introduction to Probability and Statistics

William Mendenhall, Robert J. Beaver, Barbara M. Beaver

Chapter 1

Describing Data with Graphs - all with Video Answers

Educators


Section 1

Variables and Data

01:54

Problem 1

Experimental Units Identify the experimental units on which the following variables are measured:
a. Gender of a student
b. Number of errors on a midterm exam
c. Age of a cancer patient
d. Number of flowers on an azalea plant
e. Color of a car entering a parking lot

Sheryl Ezze
Sheryl Ezze
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Problem 2

Qualitative or Quantitative? Identify each variable as quantitative or qualitative:
a. Amount of time it takes to assemble a simple puzzle
b. Number of students in a first-grade classroom
c. Rating of a newly elected politician (excellent, good, fair, poor)
d. State in which a person lives

Rashmi Sinha
Rashmi Sinha
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Problem 3

Discrete or Continuous? Identify the following quantitative variables as discrete or continuous:
a. Population in a particular area of the United States
b. Weight of newspapers recovered for recycling on a single day
c. Time to complete a sociology exam
d. Number of consumers in a poll of 1000 who consider nutritional labeling on food products to be important

Susan Hallstrom
Susan Hallstrom
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Problem 4

Discrete or Continuous? Identify each quantitative variable as discrete or continuous.
a. Number of boating accidents along a 50 -mile stretch of the Colorado River
b. Time required to complete a questionnaire
c. Cost of a head of lettuce
d. Number of brothers and sisters you have
e. Yield in kilograms of wheat from a 1 -hectare plot in a wheat field

Susan Hallstrom
Susan Hallstrom
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04:53

Problem 5

Parking on Campus Six vehicles are selected from the vehicles that are issued campus parking permits, and the following data are recorded:
$$\begin{array}{clllcc} & & & & \text { One-way } & \\& & & \text { Commute } & \text { Age of } \\& & & \text { Distance } & \text { Vehicle } \\\text { Vehicle } & \text { Type } & \text { Make } & \text { Carpool? } & \text { (miles) } & \text { (years) } \\\hline 1 & \text { Car } & \text { Honda } & \text { No } & 23.6 & 6 \\2 & \text { Car } & \text { Toyota } & \text { No } & 17.2 & 3 \\3 & \text { Truck } & \text { Toyata } & \text { No } & 10.1 & 4 \\4 & \text { Van } &\text { Dodge } & \text { Yes } & 31.7 & 2 \\5 & \text { Motor- } & \text { Hariey* } & \text { No } & 25.5 & 1 \\& \text { cycle } & \text { Davidson } & & & \\6 & \text { Car } & \text { Chevrolet } & \text { No } & 5.4 & 9\end{array}$$
a. What are the experimental units?
b. What are the variables being measured? What types of variables are they?
c. Is this univariate, bivariate, or multivariate data?

Sheryl Ezze
Sheryl Ezze
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01:16

Problem 6

Past U.S. Presidents A data set consists of the ages at death for each of the 38 past presidents of the United States now deceased.
a. Is this set of measurements a population or a sample?
b. What is the variable being measured?
c. Is the variable in part b quantitative or qualitative?

Charles Machakwa
Charles Machakwa
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02:06

Problem 7

Voter Attitudes You are a candidate for your state legislature, and you want to survey voter attitudes regarding your chances of winning. Identify the population that is of interest to you and from which you would like to sclect your sample. How is this population dependent on time?

Charles Machakwa
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Problem 8

Cancer Survival Times A medical researcher wants to estimate the survival time of a patient after the onset of a particular type of cancer and after a particular regimen of radiotherapy.
a. What is the variable of interest to the medical researcher?
b. Is the variable in part a qualitative, quantitative discrete, or quantitative continuous?
c. Identify the population of interest to the medical researcher.
d. Describe how the researcher could select a sample from the population.
e. What problems might arise in sampling from this population?

James Kiss
James Kiss
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01:46

Problem 9

New Teaching Methods An educational researcher wants to evaluate the effectiveness of a new method for teaching reading to deaf students. Achievement at the end of a period of teaching is measured by a student's score on a reading test.
a. What is the variable to be measured? What type of variable is it?
b. What is the experimental unit?
c. Identify the population of interest to the experimenter.

Charles Machakwa
Charles Machakwa
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02:03

Problem 10

Fifty people are grouped into four categories A, $B, C$, and $D$ -and the number of people who fall into each category is shown in the table:
$$\begin{array}{c|c}\text { Category } & \text { Frequency } \\\hline \mathrm{A} & 11 \\\mathrm{~B} & 14 \\\mathrm{C} & 20 \\\mathrm{D} & 5\end{array}$$
a. What is the experimental unit?
b. What is the variable being measured? Is it qualitative or quantitative?
c. Construct a pie chart to describe the data
d. Construct a bar chart to describe the data.
e. Does the shape of the bar chart in part d change depending on the order of presentation of the four categories? Is the order of presentation important?
f. What proportion of the people are in category $\mathrm{B}, \mathrm{C}$. or $\mathrm{D} ?$
g. What percentage of the people are not in category B?

Maryam Shahid
Maryam Shahid
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02:25

Problem 11

Jeans A manufacturer of jeans has plants in California, Arizona, and Texas. A group of 25 pairs of jeans is randomly selected from the computerized database, and the state in which each is produced is recorded:
$$\begin{array}{lllll}\text { CA } & \text { AZ } & \text { AZ } & \text { TX } & \text { CA } \\\text { CA } & \text { CA } & \text { TX } & \text { TX } & \text { TX } \\\text { AZ } & \text { AZ } & \text { CA } & \text { AZ } & \text { TX } \\\text { CA } & \text { AZ } & \text { TX } & \text { TX } & \text { TX } \\\text { CA } &\text { AZ } & \text { AZ } & \text { CA } & \text { CA }\end{array}$$

Sheryl Ezze
Sheryl Ezze
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Problem 12

Election 2012 During the spring of 2010 , the news media were already conducting opinion polls that tracked the fortunes of the major candidates hoping to become the president of the United States. One such poll conducted by CNN/Opinion Research Corporation Poll showed the following results:

"If Barack Obama were the Democratic Party's candidate and [see below] were the Republican Party's candidate, who would you be more likely to vote for. Obama, the Democrat, or (see below]. the Republican?" If unsure: "As of today, who do you lean more toward?
The results were based on a sample taken April $9-11$, $2010,$ of 907 registered voters nationwide.
a. If the pollsters were planning to use these results to predict the outcome of the 2012 presidential election, describe the population of interest to them.
b. Describe the actual population from which the sample was drawn.
c. Some pollsters prefer to select a sample of "likely" voters. What is the difference between "registered voters" and "likely voters"? Why is this important?
d. Is the sample selected by the pollsters representative of the population described in part a? Explain.

Victor Salazar
Victor Salazar
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02:13

Problem 13

Want to Be President? Would you want to be the president of the United States? Although many teenagers think that they could grow up to be the president, most don't want the job. In an opinion poll conducted by $A B C$ News, nearly $80 \%$ of the teens were not interested in the job. ${ }^{2}$ When asked "What's the main reason you would not want to be president?" they gave these responses:
Other career plans/no interest $\quad 40 \%$ Too much pressure Ton much work $15 \%$
Wouldn't be good at it $14 \%$
Too much arguing $5 \%$
a. Are all of the reasons accounted for in this table? Add another category if necessary.
b. Would you use a pie chart or a bar chart to graphically describe the data? Why?
c. Draw the chart you chose in part b.
d. If you were the person conducting the opinion poll, what other types of questions might you want to investigate?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:18

Problem 14

Facebook Fanatics The social networking site called Facebook has grown quickly since its inception in 2004. In fact, Facebook's United States user base grew from 42 million users to 103 million users between 2009 and $2010 .$ The table below shows the age distribution of Facebook users (in thousands) as it changed from January 2009 to January $2010 .^{3}$
$$\begin{array}{lrc}\text { Age } & \text { As of 1/04/2009 } & \text { As of 1/04/2010 } \\\hline 3-17 & 5675 & 10,680 \\8-24 & 17,192 & 26,076 \\25-34 &11,255 & 25,580 \\35-54 & 6989 & 29,918 \\55+ & 955 & 9764 \\\text { Jnknown } & 23 & 1068 \\\hline \text { fotal } & 42,089 & 103.085 \\\hline\end{array}$$
a. Define the variable that has been measured in this table.
b. Is the variable quantitative or qualitative?
c. What do the numbers represent?
d. Construct a pie chart to describe the age distribution of Facebook users as of January $4,2009 .$
e. Construct a pie chart to describe the age distribution of Facebook users as of January $4,2010 .$
f. Refer to parts $\mathrm{d}$ and e. How would you describe the changes in the age distributions of Facebook users during this 1 -year period?

Maryam Shahid
Maryam Shahid
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04:00

Problem 15

Back to Work How long does it take you to adjust to your normal work routine after coming back1.15 Back to Work How long does it take you to adjust to your normal work routine after coming back from vacation? A bar graph with data from the Snapshots section of USA Today is shown below: ${ }^{4}$
a. Are all of the opinions accounted for in the table? Add another category if necessary.
b. Is the bar chart drawn accurately? That is, are the three bars in the correct proportion to cach other?
c. Use a pie chart to describe the opinions. Which graph is more interesting to look at?

Sheryl Ezze
Sheryl Ezze
Numerade Educator