## Question 212:

1

I'm not familiar with Megastat, but you can calculate this in Excel or by hand.  The only piece of information you don't have listed here is the critical-value from the either the normal distribution or the t-distribution which you would multiple times the standard error of the mean.

Your sample is large enough (>30) that there won't be much difference between the two. To get the critical value from the normal distribution for a two-sided interval you look up .90 and .95 in the percentile to z-score calculator which provide you with 1.65 and 1.96 respectively.

The critical values for 95% and 90% from the t-distribution can be looked up in Excel by typing:

1. Men: =TINV(0.05,52) and =TINV(0.10,52) which gives you 2.006 and  1.675
2. Women: =TINV(0.05,46) and =TINV(0.10,46)  which gives you 2.013 and  1.679

Notice the number used is the Excel formula 1 less than the sample sizes--called the degrees of freedom--for a confidence interval there are n-1 degrees of freedom since we had to estimate the population mean from the sample mean.  So the difference between these critical values is pretty small (e.g. 1.96 versus 2.01).

Now you calculate the margin of error which is obtained by multiplying your standard error of the mean by these critical values. I'll be using the t-values.

1. 95% Margin of Error
• Men = 2,533.97 * 2.006 =  +/- 5083
• Women =1,815.38* 2.013 = +/- 3654
2. 90% Margin of Error
• Men = 2,533.97 * 1.675  = +/- 4244
• Women =1,815.38* 1.679 = +/- 3048

Now just add and subtract the margin of error to the mean and you're done:

1. 95% Confidence Interval
• Men = (31,410  41,576)
• Women = (20,798 28,106)
2. 90% Confidence Interval
• Men =  ( 32,249 40,737 )
• Women =(21,404  27,500 )