The city of Valley Grove is considering shortening the length of the school day. The school board hired Mr. Kent to do a survey to help them decide what to do.
a. Mr. Kent interviewed 54 students as they left the school. Is this a random sample?
My answer: Possibly, if it was out of the blue and unannounced, then it could be random.
b. Mr. Kent used this survey question: "Should the lengthy school day, which now extends to 7.5 hours, be shortened to 6 hours?" Is this question biased or fair? Support your answer.
My answer: I believe it is biased, because he emphasized how lengthy the school day was, essentially tempting the students to agree with him.
c. Of the 54 responses he received, 51 were "yes." The rest were "no." What percent of the responses were "no"?
My answer: Around 6% of the students said no.
Thanks for reading! Please check my answers.
Your answers are reasonable, but I have a suggestion for (c). Instead of stating the percentage as "around 6%," you can calculate the actual percentage using the formula (number of "no" responses / total number of responses) x 100%.
Using this formula, we have:
- Number of "no" responses = 54 - 51 = 3
- Total number of responses = 54
- Percentage of "no" responses = (3/54) x 100% = 5.56%
Therefore, the percentage of "no" responses is approximately 5.56%.
Thanks for your help and revising question (c)!
You're welcome! Feel free to reach out if you have any more math questions.
a. Your answer is correct. If Mr. Kent interviewed the students out of the blue and without any pre-selection bias, then it could be considered a random sample.
b. Your answer is also correct. The question asked by Mr. Kent is biased because it includes language that emphasizes how lengthy the school day currently is, which may influence the students to agree with the idea of shortening it. A fair question would present both sides without bias, such as "Should the school day be shortened?"
c. Your answer is incorrect. To find the percentage of students who responded "no," divide the number of "no" responses (3) by the total number of responses (54) and multiply by 100. Therefore, the percentage of "no" responses is (3/54) * 100 ≈ 5.6%.