CFA Practice Question

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CFA Practice Question

A random sample of 85 students in Chicago city high schools take a course designed to improve SAT scores. Based on these students, a 90% confidence interval for the mean improvement in SAT scores from this course for all Chicago city high school students is computed as (72.3, 91.4) points. The correct interpretation of this interval is that ______

I. 90% of the students in the sample had their scores improved by between 72.3 and 91.4 points.
II. 90% of the students in the population should have their scores improved by between 72.3 and 91.4.
Correct Answer: Neither of these statements

The confidence level states the probability that the method will give a correct answer with repeated use. In other words, if you use a 90% confidence interval often, in the long run, 90% of your intervals will contain the true parameter value. This is the proper interpretation of the confidence level.

User Contributed Comments8

User Comment
chamad what's SAT score? SAT?
JenLynn if i remember correctly it stands for scholastic aptitude test.... its a standardized exam that is taken by high school students in the US. Many US colleges require this test score as part of the college application. Although colleges consider many factors.... having a high SAT score helps get accepted to a better college
steved333 Doesn't really matter. The point is merely that a 90% confidence interval just means that you can be 90% sure that your parameter value will lie between the low and high end of the interval. SAT is just an example of how that works, that's all.
tschorsch it is the average attention span (in seconds) of a student in the Chicago Public School System
azramirza Is this correct? There is 90% confidence that the population mean of improving SAT scored is 72.3 to 91.4?
Kaloyan It means that any student enrolled in this program has "guaranteed improvement" in SAT score ranging between 72.3 and 91.4 and you can be 90 % sure that you can say this is the fact. Note there is a 10% possibility that you will have students who score outside this range, either exceeding or going lower than the range.
johntan1979 NOTE: 90% confidence interval DOES NOT mean 90% of the population

As explained by AnalystNotes above, the correct interpretation is "We are 90% confident that the true value of the parameter being estimated is within our confidence interval."
Teeto we are 90% sure that mean improvement of the SAT score for all the students who sat at the exam is between 72.3 and 91.4 point
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