Section 1.2 - Random Samples

Question 1

A ________ of n measurements from a population is a subset of the population selected in such a manner that every sample of size from the population has an equal chance of being selected.

Answer 1

simple random sample

Question 2

What are three important features of a Simple Random Sample?

Answer 2

1. Every sample of specified size n from the population has an equal chance of being selected.
2. No researcher bias occurs in the items selected for the sample.
3. A random sample may not always reflect the diversity of the population. For instance, from a population of 10 cats and 10 dogs, a random sample of size could consist of all cats.

Question 3

An easy way to select random numbers is to use a:

Answer 3

random number tell

Question 4

The term ____ should not be confused with haphazard

Answer 4

random

Question 5

How to draw a random sample:

Answer 5

1. Number all members of the population sequentially.
2. Use a table, calculator, or computer to select random numbers from the numbers assigned to the population members.
3. Create the sample by using population members with numbers corresponding to those randomly selected.

Question 6

Another important use of random-numbers is in _____.

Answer 6

Simulation

Question 7

The word simulation refers to:

Answer 7

The process of providing numerical imitations of “real” phenomena

Question 8

Sampling with replacement means:

Answer 8

although an item is selected for the sample, it is not removed from the population.

Question 9

What is Stratified Sampling?

Answer 9

Divide the entire population into subgroups (strata). Draw random samples from each stratum.

Question 10

What is Systematic Sampling?

Answer 10

Number all members of the population sequentially. Then from a random starting point, include every Kth member of the population in the sample.

Question 11

The advantage of systematic sample is that it is easy to get. However, one danger in using systematic sampling is:

Answer 11

When the population is repetitive or cyclic in nature.

Question 12

What is Cluster Sampling?

Answer 12

Divide the entire population into pre-existing segments or clusters, make a random selection of clusters. Include every member of selected cluster in the sample.

Question 13

Cluster sampling is primarily used by:

Answer 13

government agencies and certain private research organizations.

Question 14

What is Convenience Sampling?

Answer 14

Create a sample by using data from population members that are readily available.

Question 15

Convenience Sampling runs the risk of ______

Answer 15

being severely biased.

Question 16

Sampling Frame?

Answer 16

A list of individuals from which a sample is actually selected.

Question 17

Undercoverage?

Answer 17

Results from omitting population members from the Sample Frame.

Question 18

Sampling Error?

Answer 18

the difference between measurements from a sample and corresponding measurements from the respective population. It is caused by the fact that the sample does not perfectly represent the population.

Question 19

A nonsampling error is:

Answer 19

the result of poor sample design, sloppy data collection, faulty measuring instruments, bias in questionnaires, and so on.

Question 20

Explain the difference between a stratified sample and a cluster sample.

Answer 20

In a stratified sample, random samples from each stratum are included. In a cluster sample, the clusters to be included are selected at random, and then all members of each selected cluster are included.

Question 21

Explain the difference between a simple random sample and a systematic sample

Answer 21

In a systematic sample, the only samples possible are those including every kth item from the random starting position, while in a simple random sample, every sample of size n has an equal chance of being included

Question 22

Marcie conducted a study of the cost of breakfast cereal. She recorded the costs of several boxes of cereal. However, she neglected to take into account the number of servings in each box. Someone told her not to worry because she just had some sampling error. Comment on that advice

Answer 22

The advice is wrong. A sampling error accounts only for the difference in results based on the use of a sample rather than of the entire population.

Question 23

In a random sample of 50 students from a large university, all the students were between 18 and 20 years old. Can we conclude that the entire population of students at the university is between 18 and 20 years old? Explain.

Answer 23

No, even though the sample is random, some students younger than 18 or older than 20 may not have been included in the sample.

Question 24

Greg took a random sample of size 100 from the population of current season ticket holders to State College men’s basketball games. Then he took a random sample of size 100 from the population of current season ticket holders to State College women’s basketball games.

What sampling technique did Greg use to sample from the population of current season ticket holders to all State College basketball games played by either men or women?

Answer 24

Stratified.

Question 25

Greg took a random sample of size 100 from the population of current season ticket holders to State College men’s basketball games. Then he took a random sample of size 100 from the population of current season ticket holders to State College women’s basketball games.

Is it appropriate to pool the samples and claim to have a random sample of size 200 from the population of current season ticket holders to all State College home basketball games played by either men or women? Explain.

Answer 25

No, because each pooled sample would have 100 season ticket holders for men’s basketball games and for 100 women’s basketball games. Samples with, say, 125 ticket holders for men’s basketball games and 75 for women’s games are not possible.

Question 26

Suppose you are assigned the number , and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class.

(a) Explain why the first four students walking into the classroom would not necessarily form a random sample.

Answer 26

Reasons may vary. For instance, the first four students may make a special effort to get to class on time.

Question 27

Suppose you are assigned the number , and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class.

(b) Explain why four students coming in late would not necessarily form a random sample.

Answer 27

Reasons may vary. For instance, four students who come in late might all be nursing students enrolled in an anatomy and physiology class that meets the hour before in a faraway building. They may be more motivated than other students to complete a degree requirement.

Question 28

Suppose you are assigned the number , and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class.

(c) Explain why four students sitting in the back row would not necessarily form a random sample.

Answer 28

Reasons may vary. For instance, four students sitting in the back row might be less inclined to participate in class discussions.

Question 29

Suppose you are assigned the number , and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. Explain how you could get a random sample of four students from your statistics class.

(d) Explain why the four tallest students would not necessarily form a random sample.

Answer 29

Reasons may vary. For instance, the tallest students might all be male.

Question 30

Use a random-number table to generate a list of 10 random numbers between 1 and 99. Explain your work.

Answer 30

Answers vary. Use groups of two digits.

Question 31

Use a random-number table to generate a list of six random numbers from 1 to 8615. Explain your work.

Answer 31

Select a starting place in the table and group the digits in groups of four. Scan the table by rows and include the first six groups with numbers between 0001 and 8615.