In a survey of 80 high school football players who committed to play in the Division III CCIW conference, 64 said that they would work out in their high school weight rooms in the summer before college. The margin of error for the survey was 6%. A census of all CCIW football players (not just freshmen) showed that 59% worked out at their high schools. One can conclude that:
A. the subjects were less than forthcoming in their responses to the survey.
B. the sample was not representative of the population.
C. there must have been an error in the determination of the margin of error.
D. the census results are consistent with the confidence interval of the study.
is it B
I'm not sure what CCIW means, but if it involves college freshmen, then I would agree.
Yes, the correct answer is B. The sample was not representative of the population.
To understand why this answer is correct, let's break down the information provided in the question:
- In the survey of 80 high school football players who committed to play in the Division III CCIW conference, 64 stated they would work out in their high school weight rooms in the summer before college.
- The margin of error for the survey was 6%.
- A census of all CCIW football players (not just freshmen) showed that 59% worked out at their high schools.
When a margin of error is given for a survey, it represents the maximum expected difference between the survey results and the true population parameter. In this case, the margin of error is 6%, meaning that the actual percentage of high school football players who would work out in their high school weight rooms could be 6% higher or lower than the survey result.
Since the census data shows that only 59% of all CCIW football players worked out at their high schools, which is lower than the survey result of 64%, we can conclude that the sample in the survey was not representative of the entire CCIW football population. The survey sample overrepresented the percentage of players who worked out, leading to a discrepancy between the survey results and the census data.
Therefore, option B, the sample was not representative of the population, is the correct conclusion.
Yes, the correct answer is B. The sample was not representative of the population.
The fact that the survey results of 64 out of 80 high school football players committing to work out in their high school weight rooms in the summer is significantly different from the census results of 59% of all CCIW football players working out at their high schools suggests that the sample used in the survey is not representative of the wider population.