(b)A manager at a bus company wants to survey employees about the new uniforms. Which of the following best describes a convenience sample of employees?
The manager forms groups of
9
employees based on the departments the employees are in. Then, she selects all of the employees in
6
randomly chosen groups.
The manager uses a computer program to draw
54
employees at random and selects these employees. Every set of
54
employees is equally likely to be drawn by the computer program.
The manager asks for volunteers and selects every volunteer until
54
employees are selected. She selects the volunteers because these employees are easily accessible.
The manager asks for volunteers and selects every volunteer until 54 employees are selected. She selects the volunteers because these employees are easily accessible.
(c)A consultant wants to ask workers at a factory about the workers' job satisfaction. Which of the following best describes a cluster sample of workers?
The consultant forms groups of
20
workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses
4
groups and selects all of the workers in these groups.
The consultant forms
4
groups of workers based on the workers' shifts. Then, he selects
20
workers at random from each group.
The consultant takes a list of the workers and selects every
4th
worker until
80
workers are selected.
The consultant forms groups of 20 workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses 4 groups and selects all of the workers in these groups.
(a)A botanist at a nursery wants to inspect the health of the plants at the nursery. Which of the following best describes a systematic sample of plants?
The botanist assigns each plant a different number. Using a random number table, he draws
90
of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of
90
plants is equally likely to be drawn using the random number table.
The botanist forms
5
groups of plants based on the ages of the plants (in months). Then, he selects
18
plants at random from each group.
The botanist takes a list of the plants and selects every
5th
plant until
90
plants are selected.
The botanist takes a list of the plants and selects every 5th plant until 90 plants are selected.
A chemist at a pharmaceutical company wants to test the quality of a new batch of microscopes. Which of the following best describes a convenience sample of microscopes?
The chemist takes a list of the microscopes and selects every microscope until microscopes are selected.
The microscopes in the first shipment that was received are easily accessible. So, he selects all of the microscopes in this shipment.
The chemist assigns each microscope a different number. Using a random number table, he draws of those numbers at random. Then, he selects the microscopes assigned to the drawn numbers. Every set of microscopes is equally likely to be drawn using the random number table.
The microscopes in the first shipment that was received are easily accessible. So, he selects all of the microscopes in this shipment.
(c)A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a stratified sample of seats?
The supervisor forms groups of seats based on the dates the seats were last replaced. Then, she selects seats at random from each group.
All of the seats in the VIP section are easily accessible. So, the supervisor selects the seats in this section.
The supervisor forms groups of seats based on the sections the seats are in. Then, she selects all of the seats in randomly chosen groups.
The supervisor forms groups of seats based on the sections the seats are in. Then, she selects all of the seats in randomly chosen groups.
(a)A host on a cruise ship wants to collect data on the time passengers spend at various activities on board. Which of the following best describes a random sample of passengers?
The host forms groups of passengers based on the passengers' ages. Then, he randomly chooses groups and selects all of the passengers in these groups.
The host selects the first passengers who board because these passengers are easily accessible.
The host assigns each passenger a different number. Using a random number table, he draws of those numbers at random. Then, he selects the passengers assigned to the drawn numbers. Every set of passengers is equally likely to be drawn using the random number table.
The host assigns each passenger a different number. Using a random number table, he draws of those numbers at random. Then, he selects the passengers assigned to the drawn numbers. Every set of passengers is equally likely to be drawn using the random number table.
(b)A city manager wants to poll residents about a park renovation. Which of the following best describes a stratified sample of residents?
The city manager forms groups of residents based on the streets the residents live on. Then, she selects all of the residents in randomly chosen groups.
The city manager uses a computer program to draw residents at random and selects these residents. Every set of residents is equally likely to be drawn by the computer program.
The city manager forms groups of residents based on the residents' incomes. Then, she selects residents at random from each group.
The city manager forms groups of residents based on the residents' incomes. Then, she selects residents at random from each group.
(b)A city manager wants to poll residents about a park renovation. Which of the following best describes a stratified sample of residents?
The city manager forms groups of
12
residents based on the streets the residents live on. Then, she selects all of the residents in
5
randomly chosen groups.
The city manager uses a computer program to draw
60
residents at random and selects these residents. Every set of
60
residents is equally likely to be drawn by the computer program.
The city manager forms
5
groups of residents based on the residents' incomes. Then, she selects
12
residents at random from each group.
The city manager forms 5 groups of residents based on the residents' incomes. Then, she selects 12 residents at random from each group.
(c)A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a convenience sample of seats?
The supervisor takes a list of the seats and selects every
7th
seat until
56
seats are selected.
All of the seats in the VIP section are easily accessible. So, the supervisor selects the
56
seats in this section.
The supervisor forms
7
groups of seats based on the dates the seats were last replaced. Then, she selects
8
seats at random from each group.
All of the seats in the VIP section are easily accessible. So, the supervisor selects the 56 seats in this section.
Northside High wants to estimate the number of seniors who plan to go to a
4
-year college. Answer the following.
(a) Which of the following surveys probably would best represent the entire population of seniors?
25
seniors are randomly selected;
13
plan to go to a
4
-year college.
25
chess club members are randomly selected;
14
plan to go to a
4
-year college.
25
honor roll students are randomly selected from the senior class;
15
plan to go to a
4
-year college.
(b) There are
950
seniors at Northside High.
Using your answer from part (a), estimate the number of seniors who plan to go to a
4
-year college.
(a) 25 honor roll students are randomly selected from the senior class; 15 plan to go to a 4-year college.
This survey would probably best represent the entire population of seniors since honor roll students typically have high academic achievements and are more likely to pursue higher education.
(b) Since there are 950 seniors at Northside High, we can estimate the number of seniors who plan to go to a 4-year college by using the proportion from the survey in part (a).
Number of seniors who plan to go to a 4-year college = (15/25) * 950
Estimated number of seniors who plan to go to a 4-year college = 570
A political campaign wants to estimate the number of adult residents who voted in the last city election. Answer the following.
(a) Which of the following surveys probably would best represent the entire adult population of the city?
50
homeowners are randomly selected;
41
voted in the last election.
50
senior residents are randomly selected;
39
voted in the last election.
50
adult residents are randomly selected from the city;
29
voted in the last election.
(b) There are
19,300
adults who live in the city. Using your answer from part (a), estimate the number of adults who voted in the last city election.
adults
(a) 50 adult residents are randomly selected from the city; 29 voted in the last election.
This survey would probably best represent the entire adult population of the city since it involves a random selection of adult residents from the entire population.
(b) Since there are 19,300 adults who live in the city, we can estimate the number of adults who voted in the last city election by using the proportion from the survey in part (a).
Number of adults who voted in the last city election = (29/50) * 19,300
Estimated number of adults who voted in the last city election = 11,262
Washington High wants to estimate the number of students who drive to school. Answer the following.
(a) Which of the following surveys probably would best represent the entire student population?
20
students are randomly selected from the school;
5
drive to school.
20
students are randomly selected from the 11th grade;
3
drive to school.
20
students are randomly selected from the glee club;
6
drive to school.
(b) There are
1300
students at Washington High.
Using your answer from part (a), estimate the number of students who drive to school.
(a) 20 students are randomly selected from the school; 5 drive to school.
This survey would probably best represent the entire student population since it involves a random selection of students from the entire school, capturing the diversity of students.
(b) Since there are 1300 students at Washington High, we can estimate the number of students who drive to school by using the proportion from the survey in part (a).
Number of students who drive to school = (5/20) * 1300
Estimated number of students who drive to school = 325
Town officials want to estimate the number of households that own a dog. Answer the following.
(a) Which of the following surveys probably would best represent the entire population of households?
households within a mile of a park are randomly selected; own a dog.
households with a front yard are randomly selected; own a dog.
households are randomly selected from the town; own a dog.
(b) There are households in the town.
Using your answer from part (a), estimate the number of households that own a dog.
(a) households within a mile of a park are randomly selected; own a dog.
This survey would probably best represent the entire population of households since households living near a park may have a higher likelihood of owning a dog.
(b) Since the number of households in the town is not provided, it is not possible to estimate the number of households that own a dog using the given information.
Town officials want to estimate the number of households that own a dog. Answer the following.
(a) Which of the following surveys probably would best represent the entire population of households?
households within a mile of a park are randomly selected; own a dog.
households with a front yard are randomly selected; own a dog.
households are randomly selected from the town; own a dog.
(b) There are 650 households in the town.
Using your answer from part (a), estimate the number of households that own a dog.
(a) households are randomly selected from the town; own a dog.
This survey would probably best represent the entire population of households since it involves a random selection of households from the entire town, capturing the diversity of households.
(b) Since there are 650 households in the town, we can estimate the number of households that own a dog by using the proportion from the survey in part (a).
Number of households that own a dog = (proportion of households that own a dog) * 650
Without the given proportion, we are unable to provide an estimated number of households that own a dog.