Question

Statistics word problem with confidence intervals:

A statistics professor wants to compare today's students with those from 25 years ago. All of his current students marks are stored on a computer so that he can easily determine the population mean. However, the marks from 25 years ago reside only in his musty files. He does not want to retrieve all the marks and will be satisfied with a 95% confidence interval estimate of the mean mark 25 years ago. If he assumes that the population standard deviation is 12, how large a sample should he take to estimate the mean to within 2 marks?

Answer 1

In 95% of cases the population mean lies in the interval:\[xbar-1.96\frac{\sigma}{\sqrt{n}},xbar+1.96\frac{\sigma}{\sqrt{n}}\]
Subtracting and putting the result equal to 2 gives:
\[2(1.96\frac{\sigma}{\sqrt{n}})=2\]
Now just solve to find n.

Answer 2

I am assuming setting it equal to 2 was because it says "2 marks"... what is a "mark", b/c I dont see anything in the book that uses that term.

Answer 3

and I got 553.19, so is this saying that you need atleast 554 students to have 95% of them between what exactly?

Answer 4

@kropot72

Answer 5

Your answer regarding the sample size is correct. To estimate the population mean the professor needs to take a random sample of the marks of 554 students, find the total of the 554 marks and divide the total by 554 to find the sample mean mark.

Answer 6

thank you for your help, if you by chance know linear algebra, I need a little help too.

Answer 7

You're welcome :) Sorry linear algebra is not a strong area for me :(