AnswersCommon Core Math 7 - MA3107 CRSampling Methods

Sampling Methods Answers

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most

5
50 students in the art club
4
40 girls on her soccer team
2
2 students from each of the 15 classes
1
10 students from each of the 3 computer electives
2
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Kari plans to sample 20 people of a population that contains 100 students. She wants to determine how many people wake up before 6 a.m. Which sample is the most random?

A
the first 20 students who arrive at school in the morning
B
all 20 boys on the swim team
C
5 students out of each of the 4 homeroom classes
D
the last 20 people in line for breakfast in the cafeteria
3

Lamont designs a survey of town residents in an attempt to predict who will be elected mayor. He chooses his sample of 500 people from the town’s 40,000 residents by asking his question to every person leaving the public library on a Saturday. Which suggestion would most improve Lamont’s random sample?

A
Lamont should sample only adults.
B
Lamont should sample only registered voters.
C
Lamont should decrease the sample size.
D
Lamont should ask every fifth person.
4

most

T
The representative sample contained all 160 students.
T
The representative sample contained more boys than girls.
T
The representative sample contained more girls than boys.
T
The representative sample contained an equal number of boys and girls.
5

The chart below shows the distribution of weeds in a yard. A lawn-care specialist chooses a random sample from the yard and determines the number of weeds in the sample. The results of the sample are shown in the table below.Weed TypeNumberDandelion2Clover3Crab Grass2Chickweed2Which explains whether or not this is a representative sample?

Question illustration
Y
Yes, this is a representative sample because each type of weed is represented in the sample.
Y
Yes, this is a representative sample because each type of weed is represented approximately the same number of times in the sample.
N
No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
N
No, this is not a representative sample because each type of weed should be represented exactly the same number of times in the sample.
6

best

T
The sample size is not large enough to represent the population.
T
The sample was not chosen at random.
T
The way the sample was chosen may overrepresent or underrepresent students taking certain language classes.
T
The way the sample was chosen does not sample students from each different language class.
7

Samantha and Luis are attempting to determine the average number of library books that seventh-grade students check out at one time. Samantha surveys every other seventh grade student leaving the library. She samples a total of 40 of the 200 seventh graders. Luis samples 30 of the 200 seventh grade students at random in the school cafeteria. Whose sample is the most random?

A
Luis because his sample is taken from the population of all seventh graders
B
Luis because he samples fewer students
C
Samantha because she samples more students
D
Samantha because her sample is taken from the population of students who use the library
8

The chart below shows the distribution of the number of books in a library.Sahira chooses a random sample from the library and records the type of books in the chart below.Type of BookNumberFantasy10Literature25Children’s4Nonfiction11Which explains whether or not Sahira’s sample is representative?

Question illustration
N
No, it is not representative because literature books were chosen much more often than the other types.
Y
Yes, it is representative because each type of book was chosen a unique number of times.
Y
Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.
Y
Yes, it is representative because each type of book was selected as part of the sample.
9

best

N
Nathan’s because his sample was more random
J
Jordan’s because his sample was more random
N
Nathan’s because his sample contained elements of the population
J
Jordan’s because his sample contained elements of the population
10

most

T
The representative sample contained all 200 tourists.
T
The representative sample contained more adults than children.
T
The representative sample contained more children than adults.
T
The representative sample contained an equal number of adults and children.
11

Students are voting on the color of T-shirts to wear on their field trip. There are 160 students–65 boys and 95 girls–going on the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample?

A
The representative sample contained all 160 students.
B
The representative sample contained more boys than girls.
C
The representative sample contained more girls than boys.
D
The representative sample contained an equal number of boys and girls.
12

Samantha and Luis are attempting to determine the average number of library books that seventh-grade students check out at one time. Samantha surveys every other seventh grade student leaving the library. She samples a total of 40 of the 200 seventh graders. Luis samples 30 of the 200 seventh grade students at random in the school cafeteria. Whose sample is the most random?

A
Luis because his sample is taken from the population of all seventh graders
B
Luis because he samples fewer students
C
Samantha because she samples more students
D
Samantha because her sample is taken from the population of students who use the library
13

Mikayla designed a survey to determine the number of people expected at opening night of a community theater. The community has about 5,000 members. She selected a sample of the first 25 parents dropping off actors during theater rehearsal. Which best explains Mikayla’s sample?

A
random and biased
B
random and unbiased
C
nonrandom and biased
D
nonrandom and unbiased
14

Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys every other person leaving the food area. Lewie surveys every fifth person leaving the mall’s main entrance. Which set of survey results is most likely to show biased results for people who buy food at the mall?

A
Kelvin’s because he surveyed people leaving an area where food is sold
B
Kelvin’s because he surveyed every other person instead of every fifth person
C
Lewie’s because he surveyed every fifth person instead of every other person
D
Lewie’s because he surveyed people who may or may not have bought food
15

Nathan and Jordan design surveys to determine the average amount of time bicyclists in a race spend training each week. Nathan surveys every fifth bicyclist crossing the finish line after a race. Jordan surveys the first five bicyclists to finish the race. Which best explains which sample is likely to be the most valid?

A
Nathan’s because his sample was more random
B
Jordan’s because his sample was more random
C
Nathan’s because his sample contained elements of the population
D
Jordan’s because his sample contained elements of the population
16

Lamont designs a survey of town residents in an attempt to predict who will be elected mayor. He chooses his sample of 500 people from the town’s 40,000 residents by asking his question to every person leaving the public library on a Saturday. Which suggestion would most improve Lamont’s random sample?

A
Lamont should sample only adults.
B
Lamont should sample only registered voters.
C
Lamont should decrease the sample size.
D
Lamont should ask every fifth person.
17

A town hosts an Arbor Day celebration. Each of the 105 families attending gets to choose a sapling to take home as they leave. Michelle and Ari each design surveys in order to determine the average height of the saplings. Michelle samples the first 20 families leaving the celebration. Ari samples every fifth family leaving the celebration. Which best explains which student’s sample is likely to produce more valid results?

A
Michelle’s because she sampled the saplings of every family in her group
B
Michelle’s because she sampled the saplings of the first 20 families to choose their saplings
C
Ari’s because she sampled saplings chosen at different times
D
Ari’s because she sampled one more sapling than Michelle sampled
18

Perry performs a study to determine the average number of flowers on gardenia bushes at a plant nursery. Which will produce the most representative results?

A
a sample of the first 20 gardenia bushes near the entrance
B
a sample of every other gardenia bush in the shade
C
a sample of every other gardenia bush in full sun
D
a sample of 10 gardenia bushes in the shade and 10 in full sun
19

A group of tourists is determining the order in which to visit national landmarks in Washington, DC. The group contains 200 people. Of those people, 150 are adults, and 50 are children. A random sample of tourists in the group is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample?

A
The representative sample contained all 200 tourists.
B
The representative sample contained more adults than children.
C
The representative sample contained more children than adults.
D
The representative sample contained an equal number of adults and children.
20

Lorrie wants to determine the average amount of time that students at her school spend on the computer each day. There are 350 students in 15 classes. The number of boys and girls is approximately equal. Which is the most random sample?

A
50 students in the art club
B
40 girls on her soccer team
C
2 students from each of the 15 classes
D
10 students from each of the 3 computer electives

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