1.2 Data, Sampling, and Variation in Data and Sampling

1.2 Exercise 1

The data are the number of machines in a gym. You sample five gyms. One gym has 12 machines, one gym has 15 machines, one gym has 10 machines, one gym has 22 machines, and the other gym has 20 machines. What type of data is this?

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1.2 Exercise 2

The data are the areas of lawns in square feet. You sample five houses. The areas of the lawns are 144 sq. ft., 160 sq. ft., 190 sq. ft., 180 sq. ft., and 210 sq. ft. What type of data is this?

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1.2 Exercise 3

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies).

Name data sets that are quantitative discrete, quant…

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1.2 Exercise 4

The data are the colors of houses. You sample five houses. The colors of the houses are white, yellow, white, red, and white. What type of data is this?

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1.2 Exercise 5

Work collaboratively to determine the correct data type: quantitative or qualitative. Indicate whether quantitative data are continuous or discrete. Hint: Data that are discrete often start with the words the number of.

the number of pairs of shoes you own
the type of car you drive
the distance from your home to the nearest grocery store
the number of classes you take per school year
the type of ca…

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1.2 Exercise 6

Determine the correct data type, quantitative or qualitative, for the number of cars in a parking lot. Indicate whether quantitative data are continuous or discrete.

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1.2 Exercise 9

Suppose the guidance counselors at De Anza and Foothill need to make an oral presentation of the student data presented in Figures 1.5 and 1.6. Under what context should they choose to display the pie graph? When might they choose the bar graph? For each graph, explain which features they should point out and the potential display problems that might exist.

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1.2 Exercise 11

A study is done to determine the average tuition that private high school students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the fall semester. What is the type of sampling in each case?

A sample of 100 high school students is taken by organizing the students’ names by classification (freshman, sophomore, junior, or senior) and then selecti…

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1.2 Exercise 13

Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged 11 to 12, and three players from a group of boys aged 13 to 14 to form a recreational soccer team.
A pollster interviews all human resource personnel in five different high tech compa…

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1.2 Exercise 14

Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

A high school principal polls 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors regarding policy changes for after school activities.

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1.2 Exercise 15

It is unlikely that any student is in both samples.

a. Do you think that either of these samples is representative of (or is characteristic of) the entire 10,000 part-time student population?

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1.2 Exercise 16

It is unlikely that any student is in both samples.

b. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population?

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1.2 Exercise 17

$180, $50, $150, $85, $260, $75, $180, $200, $200, $150.

c. Is the sample biased?

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1.2 Exercise 18

A local radio station has a fan base of 20,000 listeners. The station wants to know if its audience would prefer more music or more talk shows. Asking all 20,000 listeners is an almost impossible task.

The station uses convenience sampling and surveys the first 200 people they meet at one of the station’s music concert events. Twenty-four people said they’d prefer more talk shows, and 176 people sa…

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1.2 Exercise 20

Use the following information to answer the next four exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.

The sampl…

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1.2 Exercise 22

Use the following information to answer the next four exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.

The color…

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1.2 Exercise 24

Use the following information to answer the next four exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.

the table…

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1.2 Exercise 26

For the following four exercises, determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

A market researcher polls every tenth person who walks into a store.

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1.2 Exercise 28

For the following four exercises, determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

A computer generates 100 random numbers, and 100 people whose names correspond with the numbers on the list are chosen.

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1.2 Exercise 30

Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Determine what the key term data refers to in the above example for Researcher A.

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1.2 Exercise 32

Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Can you tell if one researcher is correct and the other one is incorrect? Why?

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1.2 Exercise 34

Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Suggest at least two methods the researchers might use to gather random data.

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1.2 Exercise 36

Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Suppose that the second researcher conducted his survey by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method…

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1.2 Exercise 38

Would the sample size be large enough if the population is the students in the school?

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1.2 Exercise 40

Researcher A concludes that most students play video games between four and six hours each week. Researcher B concludes that most students play video games between two and four hours each week. Who is correct?

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1.2 Exercise 41

Suppose you were asked to present the data from researchers A and B in an oral presentation. When would a pie graph be appropriate? When would a bar graph more desirable? Explain which features you would point out on each type of graph and what potential display problems you would try to avoid.

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1.2 Exercise 43

Given what you know, which study is correct?

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1.2 Exercise 45

Both groups that performed the study concluded that the software works. Is this accurate?

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1.2 Exercise 47

Patients who used the software were also a part of an exercise program whereas patients who did not use the software were not. Does this change the validity of the conclusions from the exercise?

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1.2 Exercise 49

Is a sample of 500 volunteers a reliable measure for a population of 2,500?

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