Jerome wants to know how many students in his school enjoy watching comedy programs on TV. He poses this question to all 28 students in his math class and finds that 70% of his classmates enjoy watching comedy programs on TV. He claims that 70% of the school's student population would be expected to enjoy watching comedy programs on TV. Is Jerome making a valid inference about this population?

In probability, you study the chances or likelihood of a specific event occurring out of all the possible events. So, you would expect that probability is a part of a whole expressed in fractions and percentages. This is calculated from gathered statistics. Scientists gather statistical data so they could make a sound or valid representation. If the student population is over 1,000, and Jerome only gathered 28, this would not represent the majority. If Jerome really wants to know how many would enjoy comedy movies, he has to ask each and every single student of the whole population of 1,000. However, this is hardly practical. What scientists do, is they take a sample and use this to represent the whole population. Thus, Jerome should at least maybe surveyed 500 students (half of the whole) so that he could safely generalize the result to the whole student population.

Jerome's inference is invalid because his sampling technique is not random, and it may be biased.

Explanation:

A valid inference should survey a sufficiently large random sample from the school population.

A minimum sample size of 30 is recommended.

A class of math students may have habits, likes, and dislikes that are not representative of the school population.

A form of sampling such as simple or systematic sampling is more likely to yield credible inferences.