Chapter 9.2, Problem 62E

a.

To determine

To describe a completely randomized design for the experiment given which is will cash bonuses speed the return to work of unemployed people.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables. The experimental units are the smallest collection of individuals to which treatments are applied. When the units are human beings, they often are called subjects.

In an completely randomized design, the treatments are assigned to all the experimental units completely by chance. The experimental design in this example is comparative because it compares three treatments. It is randomized because the subjects are assigned to the treatments by chance.

Notice that the definition of a completely randomized design does not require that each treatment be assigned to an equal number of experimental units. It does specify that the assignment of treatments must occur completely at random.

The diagram below presents the details: random assignment, the sizes of the groups and which treatment they receive, and the response variable. This type of design is called a completely randomized design.

To implement the above design, start by labeling each people with a distinct number from 1 to 10065. Write the labels on 10065 identical slips of paper, put them in a box, and mix them well. Draw out 3355 slips. The corresponding employee will be given $500 if they found a job within 11 weeks and held it for at least 4 months. Now draw out 3355 more slips from the box. These corresponding employers will be given $500 from the state for hiring the employee. The remaining 3355 people will be given a job but no bonus for these people. At the end of the year, compare how many people got the job and corresponding bonus in the three groups.

b.

To label the subjects for random assignment.

Person 6565, 795 and 8727 are selected for treatment 1.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

Here, give each person in the experiment a unique number between 1 and 10065.

Choose a random line (127) from table D (which will be assigned during the exam).

Select the first 5-digit number.

If the number is between 00001 and 10065, then select the corresponding person for treatment 1, else ignore the number and move on to the next 5-digit number.

The first three numbers starting from line 127 in table D that are between 00001 and 10065 are: 06565, 00795 and 08727.

Thus person 6565, 795 and 8727 are selected for treatment 1.

c.

To explain the purpose of a control group in this setting.

A control group is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

Control group is used for lurking variables that might affect the response. Use a comparative design and ensure that the only systematic difference between the groups is the treatment administered.

The primary purpose of a control group is to provide a baseline for comparing the effects of the other treatments. Without such a comparison group, we wouldn't be able to tell whether the people were employed and whether they received $500 bonus or not in this experiment.

A control group here is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Answer to Problem 62E

Person 6565, 795 and 8727 are selected for treatment 1.

Explanation of Solution

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables. The experimental units are the smallest collection of individuals to which treatments are applied. When the units are human beings, they often are called subjects.

In an completely randomized design, the treatments are assigned to all the experimental units completely by chance. The experimental design in this example is comparative because it compares three treatments. It is randomized because the subjects are assigned to the treatments by chance.

Notice that the definition of a completely randomized design does not require that each treatment be assigned to an equal number of experimental units. It does specify that the assignment of treatments must occur completely at random.

The diagram below presents the details: random assignment, the sizes of the groups and which treatment they receive, and the response variable. This type of design is called a completely randomized design.

To implement the above design, start by labeling each people with a distinct number from 1 to 10065. Write the labels on 10065 identical slips of paper, put them in a box, and mix them well. Draw out 3355 slips. The corresponding employee will be given $500 if they found a job within 11 weeks and held it for at least 4 months. Now draw out 3355 more slips from the box. These corresponding employers will be given $500 from the state for hiring the employee. The remaining 3355 people will be given a job but no bonus for these people. At the end of the year, compare how many people got the job and corresponding bonus in the three groups.

b.

To determine

To label the subjects for random assignment.

Person 6565, 795 and 8727 are selected for treatment 1.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

Here, give each person in the experiment a unique number between 1 and 10065.

Choose a random line (127) from table D (which will be assigned during the exam).

Select the first 5-digit number.

If the number is between 00001 and 10065, then select the corresponding person for treatment 1, else ignore the number and move on to the next 5-digit number.

The first three numbers starting from line 127 in table D that are between 00001 and 10065 are: 06565, 00795 and 08727.

Thus person 6565, 795 and 8727 are selected for treatment 1.

c.

To explain the purpose of a control group in this setting.

A control group is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

Control group is used for lurking variables that might affect the response. Use a comparative design and ensure that the only systematic difference between the groups is the treatment administered.

The primary purpose of a control group is to provide a baseline for comparing the effects of the other treatments. Without such a comparison group, we wouldn't be able to tell whether the people were employed and whether they received $500 bonus or not in this experiment.

A control group here is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Answer to Problem 62E

Person 6565, 795 and 8727 are selected for treatment 1.

Explanation of Solution

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

Here, give each person in the experiment a unique number between 1 and 10065.

Choose a random line (127) from table D (which will be assigned during the exam).

Select the first 5-digit number.

If the number is between 00001 and 10065, then select the corresponding person for treatment 1, else ignore the number and move on to the next 5-digit number.

The first three numbers starting from line 127 in table D that are between 00001 and 10065 are: 06565, 00795 and 08727.

Thus person 6565, 795 and 8727 are selected for treatment 1.

c.

To determine

To explain the purpose of a control group in this setting.

A control group is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Explanation:

Control group is used for lurking variables that might affect the response. Use a comparative design and ensure that the only systematic difference between the groups is the treatment administered.

The primary purpose of a control group is to provide a baseline for comparing the effects of the other treatments. Without such a comparison group, we wouldn't be able to tell whether the people were employed and whether they received $500 bonus or not in this experiment.

A control group here is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Answer to Problem 62E

A control group is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.

Explanation of Solution

Given Information:

The Illinois Department of Employment Security designed an experiment to find out will cash bonuses speed the return to work of unemployed people. The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11 weeks and held it for at least 4 months. Others could tell potential employers that the state would pay the employer $500 for hiring them. A control group got neither kind of bonus.

Control group is used for lurking variables that might affect the response. Use a comparative design and ensure that the only systematic difference between the groups is the treatment administered.

The primary purpose of a control group is to provide a baseline for comparing the effects of the other treatments. Without such a comparison group, we wouldn't be able to tell whether the people were employed and whether they received $500 bonus or not in this experiment.

A control group here is used to eliminate outside effects that can occur due to chance, the environment, the employers etc.