A recent survey of students found that 70% of the students in the sample said th
ID: 3231310 • Letter: A
Question
A recent survey of students found that 70% of the students in the sample said that they are not satised with the state of race relations in the U.S. The poll’s margin of error for 95% condence was 3%. This means that
(A) we can be sure that the percent of all students who are not satised with the state of race relations in the U.S. is between 67% and 73%.
(B) the survey used a method that gets an answer within 3% of the truth about the population 95% of the time.
(C) another survey of students using the same method would produce results that will lie between 67% and 70%.
(D) there is a 95% chance that 70% will be within±3%. (E) the survey wasn’t conducted correctly 3% of the time and this can be stated with 95% probability
Explanation / Answer
Margin of error of plus or minus E at a level of conficence of x%, means that when that method is used over and over, in x% of all cases, the true value of th parameter will be within E of the statistic.
The margin of error would mean that the true proportion would be within the margin of error of the sample proportion.
In about 95% of all random samples of this size from the same population, the difference between the sample percent and the population percent will be less than 3%.Hence the answer is Option (B)
The survey used a method that gets an answer within 3% of the truth about the population 95% of the time.