A researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 30 students: 12 of them supported the change, 13 of them did not, and 5 had no opinion. This is not a binomial model because...
A. ...there are 3 possible outcomes, not 2.
B. ...the students who strongly supported the change and those who only mildly supported the change are counted the same.
C. ...less than half of the students supported the change.
D. 30 students are not enough for a good sample
Some of the requirements of a binomial model are:
1. probability of success is known and does not vary over the experiment
2. Has exactly two outcomes (head/tail, success/failure).
3. has one or multiple steps
4. is a random experiment
The correct answer is A. ...there are 3 possible outcomes, not 2.
In a binomial model, there are only two possible outcomes for each trial, typically referred to as "success" and "failure." However, in this case, there are three possible outcomes: support, no support, and no opinion. Therefore, it cannot be considered a binomial model.
Option B is not correct because the way the students' level of support is counted does not determine whether the model is binomial or not. In a binomial model, the outcomes are only classified as success or failure, not based on the degree of support.
Option C is not correct because the proportion of students who supported the change is not a determining factor in whether the model is binomial or not. Binomial models can still be used even when the outcome is not evenly split.
Option D is not correct because the sample size of 30 students can still be sufficient for analyzing data and drawing conclusions in many cases. The suitability of the sample size depends on various factors such as the research question, population size, and desired level of precision.