Quick Question on Two Tailed Tests

CFA Level I Quant
#1

Heres the question:

Use the following values from Student’s t-distribution to establish a 95% confidence interval for the population mean given a sample size of 10, a sample mean of 6.25, and a sample standard deviation of 12. Assume that the population from which the sample is drawn is normally distributed and the population variance is not known.

The answer involves finding the correct t stat using the table. I am curious what in the question tells us we need to use a p-value of .025 instead of .05.

Is it because the data is normally distributed?

#2

This is not a “test” question (i.e., you’re not testing an hypothesis); it’s a confidence interval question.

Confidence intervals (as far as CFA Institute is concerned) are always centered about the mean.

#3

So, for CFA purposes, in using the t stat table (degrees of freedom on the left and p-value at the top), we should look up the t-stat under p=.025 for any confidence interval question. Is that right?

#4

Or more accurately alpha/2

#5

When they said 95% confidence interval, it means that there’s a probability of 5% that the population mean is outside your confidence interval.

“Outside” can be above or below your confidence interval. Therefore, you need to account for the top and bottom values.

That’s why it’s 5%/2, and not 5%. So you’ll have 2.5% on either side, which add up to 5% overall.

#6

If they said 95%, you’d use p = 5%/2 = 0.05/2 = 0.025.

If they said 99%, you’d use p= 1%/2 = 0.01/2 = 0.005.