Question

discuss the statement and tell what possible misuse or misinterpretation may exist.

thirty students said that they would recommend professor wilson to a friend. twenty students said that they would recommend professor jaffe to a friend. therefore, professor wilson is a better teacher than professor jaffe.

discuss the statement and tell what possible misuse or misinterpretation may exist. choose the correct answer below.

a. the statement is not valid because if more students prefer a teacher it means that teacher is better and student opinion does not matter to determining the quality of a professors teaching abilities.
b. the statement is not valid because we dont know how many of each professors students were surveyed and student opinion does not necessarily determine the quality of a professors teaching abilities.
c. the statement is valid because if more students prefer a teacher it means that teacher is better and student opinion determines the quality of a professors teaching abilities.
d. the statement is valid because we dont know how many of each professors students were surveyed and student opinion determines the quality of a professors teaching abilities.

Explanation:

Analyze the given statement

Using the Statistical Misinterpretation knowledge point

The statement compares absolute numbers of students (30 vs. 20) who recommend two professors without knowing the total number of students surveyed for each. This represents a classic misinterpretation of raw counts versus proportions.

Evaluate the validity of the conclusion

Using the Statistical Misinterpretation knowledge point

The conclusion that Professor Wilson is a better teacher is invalid because:

1. We do not know the sample sizes (e.g., 30 out of 300 is \(10\%\), while 20 out of 20 is \(100\%\)).
2. Student recommendation opinions do not directly measure objective teaching quality.

Match with the correct option

Using the Statistical Misinterpretation knowledge point

Option B correctly identifies both flaws: the unknown sample sizes and the subjective nature of student opinions in determining teaching quality.

Answer:

• A. The statement is not valid because if more students prefer a teacher it means that teacher is better and student opinion does not matter to determining the quality of a professor's teaching abilities.
• B. The statement is not valid because we don't know how many of each professor's students were surveyed and student opinion does not necessarily determine the quality of a professor's teaching abilities. (Correct answer)
• C. The statement is valid because if more students prefer a teacher it means that teacher is better and student opinion determines the quality of a professor's teaching abilities.
• D. The statement is valid because we don't know how many of each professor's students were surveyed and student opinion determines the quality of a professor's teaching abilities.