Calculate confidence interval

Calculate confidence interval.?

A researcher wants to find the average IQ of a group of students. She randomly samples 100 people and obtains the following results.

Mean = 106.5
SD = 12.0

Calculate 95% confidence interval for the mean IQ of the students.

What does this confidence interval mean?

***PLEASE help me answer this---show your work so I can understand. Thanks!

Other Answers:

Sample mean 106.5
Standard deviation = 12
Standard error of mean = sd / sqrt(n)
SE = 12/10
Standard error of mean 1.2
Confidence limits 106.5-(1.2)(1.984)
and 106.5+(1.2)(1.984)
95 % limits (104.1192,108.8808)
1.984 is the critical t-value with 99 degrees of freedom as we are estimating the population standard deviation frm the sample.
The interval means we are 95 % sure (or confident) that the true mean of all of the students lie somewhere between 104.12 and 108.88.

To nitpick with cidyah above, he isn't wrong, but few would bother to use the t-distribution with samples that large and with SD calculated from many such samples. The normal distribution would typically be used, and the intervals would be 1.96 SEs wide.

Also, the statistics police will get ya' if you use his definition of confidence interval. We are 95% confident that the interval contains the true mean, not that the true mean is within the interval. While it's admittedly a nit, probabilistic statements must be made about statistics (random variables). The limits are statistics; the true mean is not. Said another way, the probability is about our ability to construct such an interval, not about what the true mean is.

An even more rigorous definition is that if we repeated this procedure a great many times, we would construct intervals that enclose the true mean 95% of the time. So for any particular procedure, there is a 95% probability that the interval contains the true mean.