Question

select the correct answer.

a piano teacher is interested in knowing how many of her students plan to take time off from lessons during the summer months. she surveys each student on monday and determines that about 50% of her students plan to take time off.

she then repeats her study with her students on tuesday, wednesday, thursday, and friday. all surveys yield the same results. what generalization can the piano teacher make?

most of her students plan to take time off this summer.
about half of her students plan to take time off this summer.
there is not enough information to generalize the survey results.
the sample is biased; therefore, a generalization cannot be made regarding how many of her students plan to take time off this summer.

Explanation:

Analyze the survey methodology

The piano teacher surveys each of her students on Monday, and then repeats this by surveying each of her students on Tuesday, Wednesday, Thursday, and Friday. This means she has surveyed her entire population of students (every student she teaches across all weekdays).

Evaluate the sample representation

Because she surveyed every single student in her entire student population across all days of the week, there is no sampling involved. She conducted a census of her entire student population rather than taking a sample. Therefore, there is no sampling bias.

Determine the valid generalization

Since she collected data from 100% of her students and every daily survey yielded the same result (about 50%), she can accurately conclude that about half of her entire student population plans to take time off this summer.

Compare with the given options

• "Most of her students plan to take time off this summer": Incorrect, as 50% represents half, not "most".
• "About half of her students plan to take time off this summer": Correct, as this directly reflects the 50% result obtained from surveying all her students.
• "There is not enough information to generalize the survey results": Incorrect, because she surveyed her entire student body.
• "The sample is biased...": Incorrect, because she surveyed all her students, meaning she has census data rather than a biased sample.

Answer:

• (A) Most of her students plan to take time off this summer.
• (B) About half of her students plan to take time off this summer. (Correct answer)
• (C) There is not enough information to generalize the survey results.
• (D) The sample is biased; therefore, a generalization cannot be made regarding how many of her students plan to take time off this summer.