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.
What I have to answer:
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. It is not clear if Mr. Kent's sample of 54 students is a random sample. A random sample would be selected in such a way that every student in the school has an equal chance of being included in the sample. Without more information about how Mr. Kent selected the 54 students, it is not possible to determine if this is a random sample or not.
b. The survey question used by Mr. Kent is biased because it includes the phrase "lengthy school day." This phrase suggests that the current length of the school day is a problem or burden, which could influence respondents to favor a shorter day. A more neutral question would ask something like "Do you think the school day should be shortened?"
c. Of the 54 responses, 3 were "no." To find the percent of responses that were "no," we can use the formula:
no responses / total responses * 100%
In this case, we have:
3 / 54 * 100% = 5.6%
So 5.6% of the responses were "no."