Question

Help me understand this problem, I have several more like this & want to get an understanding on to solve it:

The mean score,x, on an aptitude test for a random sample of 9 students was 64. Assuming that standard deviation=16, construct a 95.44% confidence interval for the mean score of all students taking the test.

A. 53.3 to 74.7 B. 60.4 to 67.6 C. 32 to 96 D. 56.0 to 72.0

Answer 1

The standard error of the mean (SEM) is the standard deviation divided by the square root of the sample size - which in this instance is 9 - so the SEM here is 16/sqrt(9)=5.33.

The question actually contains a little clue that you're probably on the right track in that very specific figure of 95.44% for a confidence interval - because if you look up that figure in a set of Normal probability tables, you should find that it corresponds to a very convenient Z value.

Your confidence interval will then range from (M - 5.33*Z) to (M + 5.33*Z).