posted by Lexie on .
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
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).