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? Explain.
b. Mr. Kent used this survey question: “Should the lengthy school day, which now extends for 7.5 hours, be shortened to 6 hours?” Is this question biased or fair? Explain.
c. Of the 54 responses he received, 51 were “yes.” The rest were “no.” What percent of the responses were “no”?
a. This sample may not be considered random because the sample group selected consists only of students leaving the school. There could be a bias towards a certain age group or type of student who leave the school at a particular time. In addition, students who are absent or have other commitments on the day of Mr. Kent's survey may be excluded from the sample group.
b. This question may be considered biased because it uses the word "lengthy" to describe the school day, which implies that the current length is undesirable or too long. It would be more neutral to simply state the current length of the school day and ask for opinions on whether it should be shortened.
c. Since 51 out of 54 responses were “yes,” the percent of responses that were “no” can be calculated as follows:
Percentage of “no” responses = (Number of “no” responses ÷ Total number of responses) × 100
Percentage of “no” responses = (3 ÷ 54) × 100
Percentage of “no” responses ≈ 5.6%
Therefore, approximately 5.6% of the responses were “no.”