Homework 2

What is a​ frame?

1. Choose the correct answer below.

1. A frame is the sample taken from the population being studied.
2. A frame is a list of the individuals in the population being studied.
3. A frame is the population being studied.
4. A frame is a list of the individuals in the sample being studied.

2.  Define simple random sampling.

Choose the correct answer below.

1. Simple random sampling is the process of using chance to select individuals from a population to be included in the sample. The sample is then called a simple random sample.
2. Simple random sampling is the process of selecting individuals from a population using a convenient sample. The sample is then called a simple random sample.
3. Simple random sampling is the process of obtaining a sample of size n from a population of the same size n. The sample is then called a simple random sample.
4. A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

3.  What does it mean when sampling is done without​ replacement?

Choose the correct answer below.

1. Once a sample is​ taken, those individuals cannot be selected for any other samples.
2. Once an individual is​ selected, the individual cannot be selected again.
3. Once a sample is​ taken, those individuals are no longer considered part of the population.
4. Once an individual is​ selected, the individual can be selected again.

4. 

As part of a college literature​ course, students must select three classic works of literature from the provided list and complete critical book reviews for each selected work. Write a short description of the processes that can be used to generate a simple random sample of three books. Obtain a simple random sample of size 3 from this list.

Which of the following would produce a simple random​ sample? Select all that apply.

1. Ask someone their opinion on which three books are​ best, and select those three.
2. List each book on a separate piece of​ paper, place them all in a​ hat, and pick three.
3. List the names in alphabetical order and take the first three on the list.
4. Number the books from 1 to 9 and use a random number table to produce 3 different one digit numbers corresponding to the books selected.

Use the portion of the random number table provided below to obtain a simple random sample of size 3 from this list. If you start on the left and take the first three numbers between 1 and​ 9, what three books would be selected from the numbered​ list?

91911, 66146, 75789

1. A Tale of Two Cities, The Sun Also Rises, As I Lay Dying
2. The Sun Also Rises, The Scarlet Letter, Huckleberry Finn
3. A Tale of Two Cities, The Sun Also Rises, A Tale of Two Cities
4. The Scarlet Letter, Huckleberry Finn, As I Lay Dying
5. A Tale of Two Cities, The Sun Also Rises, The Scarlet Letter

5. As part of a college literature​ course, students must read three classic works of literature from the provided list. Write a short description of the processes that can be used to generate a simple random sample of three books. Obtain a simple random sample of size 3 from this list.

Which of the following would produce a simple random​ sample? Select all that apply.

1. Number the books from 1 to 9 and use a random number generator to produce 3 different numbers from 1 to 9 that correspond to the books selected.
2. Ask someone their opinion on which three books are​ best, and select those three.
3. List the names in alphabetical order and take the first three on the list.
4. List each book on a separate piece of​ paper, place them all in a​ hat, and pick three.

The list of digits below is from a random number generator using technology. Use the list of numbers to obtain a simple random sample of size 3 from this list. If you start on the left and take the first three numbers between 1 and​ 9, what three books would be selected from the numbered​ list?

1​, 6​, 6​, 6​, 6​, 4​, 0​, 4​, 9​, 4​, 8​, 5​, 5​, 8​, 6

1. Pride and Prejudice, As I Lay Dying, As I Lay Dying
2. The Scarlet Letter, The Sun Also Rises, Crime and Punishment
3. Pride and Prejudice, As I Lay Dying, The Scarlet Letter
4. Pride and Prejudice, As I Lay Dying, Crime and Punishment
5. As I Lay Dying, The Scarlet Letter, The Sun Also Rises

6.  A community college employs 89 ​full-time faculty members. To gain the​ faculty’s opinions about an upcoming building​ project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 89.

Complete parts​ (a) and​ (b) below.

​(a) Using the provided random number​ table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row​ 3, column 6. Using this position as the starting point and proceeding​ downward, determine the numbers for the 9 faculty members who will be included in the sample.

The numbers for the faculty members are

(b) The president uses technology to produce the following random numbers.

21 72  67  36  13  72  66  86  52  76

Determine the numbers for 9 faculty members who will be included in the sample.

The numbers for the faculty members are _____

7.  Suppose you are the president of the student government. You wish to conduct a survey to determine the student​ body’s opinion regarding student services. The administration provides you with a list of the names and phone numbers of the 750 registered students.

​(a) Discuss a procedure you could follow to obtain a simple random sample of 5 students.

​(b) Obtain this sample.

(a) Which of the following procedures could you follow to obtain a simple random sample of 5 ​students? Select all that apply.

1. Number the names from 1 to 750 and use a random number table to produce 5 different​ three-digit numbers corresponding to the names selected.
2. Ask the students to come to a meeting and pick five from those who come to the meeting.
3. List the names in alphabetical order and take the first five names on the list.
4. List each name on a separate piece of​ paper; place them all in a​ hat, and pick five.

​(b) Obtain this sample using the portion of the random number table provided in the problem statement. Start with the first column of the first row and work down each column.

Type the numbers corresponding to the students chosen.

8.  Which sampling method does not require a​ frame?

Choose the correct answer below.

1. Simple random
2. Stratified
3. Cluster
4. Systematic
5. All of the above sampling methods require a frame

9.  ​A(n)  ______ is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.

10. A(n) _____ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.

11.  Determine whether the following statement is true or false. Explain.

A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size.

Choose the correct answer below.

1. ​True, because it does not require extra preparation and can return more information than the other sampling techniques.
2. ​False, because other sampling techniques may provide more information for less cost than a simple random sample.
3. ​True, because every individual has an equal chance of selection.
4. ​False, because simple random samples require a larger sample size than most other sampling methods.

12.  Determine whether the following statement is true or false. Explain. When conducting a cluster​ sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.

Choose the correct answer below.

1. False. It is better to have fewer clusters when the clusters are homogeneous.
2. ​False, because the proportion of individuals per cluster to the population should not be affected by whether or not the clusters are heterogeneous.
3. ​True, because heterogeneous clusters are not likely to resemble population​ heterogeneity, increasing the number of necessary individuals.
4. ​True, because when the clusters are​ heterogeneous, they are scaled down versions of the population.

13.  Determine whether the following statement is true or false. Explain. Inferences based on voluntary response samples are generally not reliable.

Choose the correct answer below.

1. ​False, because individuals who volunteer are least likely to have personal bias.
2. ​False, because a surveyor cannot force volunteers to respond.
3. ​True, because it is often the case that the individuals who volunteer do not accurately represent the population.
4. ​True, because the group that volunteers may not be a large enough sample size.

14.  Determine whether the following statement is true or false. Explain.When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal.

Choose the correct answer below.

1. False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
2. False. When taking a stratified​ sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.
3. True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample.
4. False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this​ process, it is unlikely that all strata will be sampled from the same number of times.

15.  To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at Sony selects every 13th music CD that comes off the assembly line starting with the fifth until she obtains a sample of 50 music CDs. What type of sampling is​ used?

1. Systematic
2. Convenience
3. Cluster
4. Stratified
5. Simple random

16. To determine customer opinion of their safety features​, Toyota randomly selects 100 dealerships

during a certain week and surveys all customers visiting the dealerships. What type of sampling is​ used?

1. Stratified
2. Systematic
3. Cluster
4. Simple random
5. Convenience

17. Microsoft wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company.

What type of sampling is​ used?

1. Cluster
2. Simple random
3. Stratified
4. Systematic
5. Convenience

18.  A radio station asks its listeners to call in their opinion regarding the format of the morning show. What type of sampling is​ used?

1. Cluster
2. Systematic
3. Simple random
4. Convenience
5. Stratified

19   To determine her water pressure​, Jean divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her water pressure at 2 randomly selected times during each part of the day.

What type of sampling is​ used?

1. Stratified
2. Convenience
3. Cluster
4. Systematic
5. Simple random

20. For a poll of voters regarding a referendum calling for a national health care program​, design a sampling method to obtain the inviduals in the sample. Be sure to support your choice. Which sampling method would most likely be used in a poll of voters regarding a referendum calling for a national health care program​?

1. Use systematic random sampling. By varying the​ k-value, a sampling of the whole nation can be selected to achieve the needed accuracy.
2. Use stratified random sampling. Since this is a national​ issue, different geographical locations are likely to have similar views.
3. Use cluster sampling. Each geographical region can be treated as a​ mini-population because voting results are independent of region.
4. Use simple random sampling. Simple random sampling is always the best sampling method to choose regardless of the survey conducted.
5. Use convenience sampling. A large number of voters is needed to accurately reflect the​ nation’s voters; so a quick way to collect information is needed.

21.  Suppose a marketing firm wants to gather information about a new product. The firm divided a city into blocks as illustrated.​ (Note: the numbers shown represent house address​ numbers.) Which of the following represents a possible cluster sample of the homes in the​ city?

​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.)

Choose the correct answer below.

1. 1325​,1326​,1536​,1629​,1494​,6581​,9018​,8102
2. 6577​,1492​,1628​,7310​,9015​,8107​,1323​,1533
3. 7303,7306,7307,7310,7311,7314,7315,7318
4. 1498​,1626​,1328​,9014​,1498​,7307​,1535​,

22. A professor wants to randomly select 4 students to go to the board. She decides to randomly select the third student who enters the classroom and every sixth student after that. Determine the students who will be going to the board. Write down the student numbers.

The numbers of the students that will be going to the board are

23  Suppose the size of a population is N=7000 and the sample size desired is n=19.

What value of k should be used to obtain a systematic sample from this​ population?