Finding and interpreting a confidence interval for a population mean with σ known

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we’re going to learn how to find and interpret a confidence interval for a population mean with sigma known.  Here’s our problem statement: Salaries of 42 college graduates who took a statistics course in college had a mean value of $64,300.  Assuming a standard deviation of $16,562, construct a 99% confidence interval for estimating the population mean mu.

Solution

OK, because we know what sigma is (just the standard deviation for the population), we’re going to use a Normal distribution; we’re going to calculate z-scores.  So to do that, I’m going to pull up StatCrunch.  I could use the z-score tables, but my preference is to use StatCrunch.  So inside StatCrunch, I’m going to go to Stat –> Calculators — excuse me, I’m going to go to Z Stats –> One Sample (because I’ve only got one sample I’m looking at) –> With Summary (because we don't have actual data, just summary statistics).

Here I’m going to put in the values that they give me here in the problem statement.  There’s my mean value, there’s the standard deviation, there's the sample size.  And now, because I want a confidence interval, I’m going to click the radio button here next to “Confidence Interval.”  And we want a 99% confidence interval, so I need to change this default from 95 to 99.  I hit Compute! É viola!  There's my lower and upper limit for my confidence interval.  So I simply slip those values here into my answer fields.  I want to round to the nearest integer.  Excellent!

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