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

A group of test subjects is divided into twelve groups; then four of the groups are chosen at random.

Short Answer

Expert verified

The sampling method used for the given case is cluster sampling.

Step by step solution

01

Concept Introduction

Sampling, in statistics, is the process of learning about a population based on a sample selected from the population of interest.

02

Explanation

For sampling, the sample can be chosen in a variety of ways. The following are some of the most important sampling methods:

  • Simple random sampling: It is the type of sampling in which every unit of the population has an equal chance of being included in the sample. The sample is chosen at random by the researcher using various procedures such as a random number table and the lottery method.
  • Systematic sampling: In this method, the investigator selects a starting point from the population at random and then selects every nth data point from the population's listing.
  • Stratified sampling: In this method of sampling, the investigator divides the entire population into homogeneous groups (known as strata) depending on particular criteria, and then selects a sample from each of these strata at random.
  • Cluster sampling: It is a technique in which the researcher divides the population into many clusters and then selects some of the clusters at random. All members of the selected clusters are investigated.
  • Convenience sampling: It's a method of sampling that isn't done at random. Subjects that are readily available are chosen in this form of sampling. For example, an online poll was performed to gauge public opinion on the introduction of a new product to the market.

In the given example, the researcher splits the test subjects into twelve groups in order to answer the question, and then four groups are picked at random. As a result, cluster sampling was chosen as the sampling method.

03

Final answer

Hence, for the given example, the sampling method used is cluster sampling.

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Most popular questions from this chapter

Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. Two researchers each follow a different set of 40 patients with AIDS from the start of treatment until their deaths. The following data (in months) are collected.

Researcher A:

3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 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

Determine what the key terms refer to in the example for Researcher A.

statistic

How much time does it take to travel to work? Table 1.36shows the mean commute time by state for workers at least 16years old who are not working at home. Find the mean travel time, and round off the answer properly.

Use the following information to answer the next seven exercises: Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.

Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 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

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

Use the following information to answer the next seven exercises: Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.

Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 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

Suppose that the first researcher conducted his survey by randomly choosing one state in the nation and then randomly picking 40 patients from that state. What sampling method would that researcher have used?

1.11 You are going to use the random number generator to generate different types of samples from the data.

This table displays six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class.

Instructions: Use the Random Number Generator to pick samples.

1. Create a stratified sample by column. Pick three quiz scores randomly from each column.

◦ Number each row one through ten.

◦ On your calculator, press Math and arrow over to PRB.

◦ For column 1, Press 5:randInt( and enter 1,10). Press ENTER. Record the number. Press ENTER 2 more

times (even the repeats). Record these numbers. Record the three quiz scores in column one that correspond

to these three numbers.

◦ Repeat for columns two through six.

◦ These 18 quiz scores are a stratified sample.

2. Create a cluster sample by picking two of the columns. Use the column numbers: one through six.

◦ Press MATH and arrow over to PRB.

◦ Press 5:randInt( and enter 1,6). Press ENTER. Record the number. Press ENTER and record that number.

◦ The two numbers are for two of the columns.

◦ The quiz scores (20 of them) in these 2 columns are the cluster sample.

3. Create a simple random sample of 15 quiz scores.

◦ Use the numbering one through 60.

◦ Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).

◦ Press ENTER 15 times and record the numbers.

◦ Record the quiz scores that correspond to these numbers.

◦ These 15 quiz scores are the systematic sample.

4. Create a systematic sample of 12 quiz scores.

◦ Use the numbering one through 60.

◦ Press MATH. Arrow over to PRB. Press 5:randInt( and enter 1, 60).

◦ Press ENTER. Record the number and the first quiz score. From that number, count ten quiz scores and

record that quiz score. Keep counting ten quiz scores and recording the quiz score until you have a sample

of 12 quiz scores. You may wrap around (go back to the beginning).

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