A behavioral psychologist plans an experimental sleep study with college students. Which statements about this experiment must be true in order to use a binomial model?
Select all that apply.
HELP PLEASE
Each trial is independent.
There is an equal number of male and female students.
The only possible outcomes are wake-up or sleep.
Subjects are either first- or second-year college students.
The number of trials is fixed in advance.
Observers are not in the same room as the sleeping students.
Subjects must sign a human study release form.
each trial is independent
the only possible outcomes are wake-up or sleep
the number of trials is fixed in advance
The statements that must be true in order to use a binomial model for this experiment are:
1. Each trial is independent.
2. The only possible outcomes are wake-up or sleep.
3. The number of trials is fixed in advance.
So, the correct statements are:
- Each trial is independent.
- The only possible outcomes are wake-up or sleep.
- The number of trials is fixed in advance.
To determine which statements about the experiment must be true in order to use a binomial model, let's analyze each statement:
1. Each trial is independent: This statement must be true in order to use a binomial model. Each trial's outcome should not depend on the outcome of previous or future trials. In the sleep study, each student's sleep/wake-up outcome should not be influenced by the outcomes of other students' sleep/wake-up patterns.
2. There is an equal number of male and female students: This statement is not essential for using a binomial model. The equal number of males and females can be helpful for balancing the sample groups, but it is not a requirement for a binomial model.
3. The only possible outcomes are wake-up or sleep: This statement is important for using a binomial model. In a binomial experiment, there should be only two mutually exclusive and collectively exhaustive outcomes (in this case, waking up or sleeping) for each trial.
4. Subjects are either first- or second-year college students: This statement is not directly relevant to using a binomial model. The classification of subjects into first- or second-year college students does not impact whether or not a binomial model can be used.
5. The number of trials is fixed in advance: This statement is necessary for using a binomial model. In a binomial experiment, the number of trials (e.g., the number of students examined) should be predetermined and fixed.
6. Observers are not in the same room as the sleeping students: This statement is not directly relevant to using a binomial model. The physical arrangement of observers and sleeping students does not impact whether or not a binomial model can be used.
7. Subjects must sign a human study release form: This statement is not essential for using a binomial model. It is related to ethical considerations and compliance with research regulations, but it does not affect the application of a binomial model.
Therefore, the statements that must be true in order to use a binomial model are:
- Each trial is independent.
- The only possible outcomes are wake-up or sleep.
- The number of trials is fixed in advance.
Remember, a binomial model is appropriate when the experiment satisfies the conditions of independence, two mutually exclusive outcomes, and a fixed number of trials.