12. On a college campus, a survey randomly polled 537 students and asked them wh
ID: 3135018 • Letter: 1
Question
12. On a college campus, a survey randomly polled 537 students and asked them whether or not they feel safe on campus. 50.89% of the students said they feel safe on campus, leading to the University Chronicle headline “A majority of our students feel safe on campus for the first time”. A 95% confidence interval for the proportion of students who feel safe on campus is (0.476, 0.528). Does this interval support the claim of the University Chronicle? a. No; the confidence interval includes values which are less than 0.5. Hence, there is a possibility that the proportion of students who feel safe is actually less than 0.5 b. Yes; the confidence interval contains values which are strictly greater than 0. Hence, there is a possibility that the proportion of students who feel safe is indeed greater than 0. c. Yes; the point estimate of 50.89% is included in the interval, so it is reasonable to assume that the proportion of students who feel safe is at least 0.5. d. Yes; the confidence interval barely contains 50.89%, so it is reasonable to assume that the proportion of students who feel safe is greater than 0.5
Explanation / Answer
IN THIS QUESTION WE HAVE BEEN GIVEN THE CONFIDENCE INTERVAL AND THE CLAIM OF THE UNIVERSITY IS ALSO GIVEN WE NEED TO JUDGE THE CLAIM OF THE UNIVERSITY.
THE CONFIDENCE INTERVAL TELLS THAT THE MEAN OF THE SAMPLE MUCH BE IN THE INTERVAL AND THE EXTREAME VALUE OF THE INTERVAL ARE NOT THE MEAN.
AS PER THE UNIVERSITY CLAIM THAT 50.89% ARE FEELING SAFE WHICH MEANS THAT 0.5089 SHOULD BE WELL CONTAINED IN THE INTERVAL FOR THE HEADLINE TO BE TRUE
AS PER THE INTERVAL THE 0.5089 IS IN THE INTERVAL AND SOME WHAT IS BETWEEN THE MID POINT OF THE INTERVAL HENCE THE HEADLINE IS TRUE AND OPTION C IS CORRECT.
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