### Z - Confidence Interval

Always start each new problem from the home screen

Say we want to develop a 95% confidence interval for the population mean from a sample size of 35 where we know the sample mean is 100 and the population deviation is 12. For this problem we want Z-Interval because we are given sigma.

On the calculator we will choose "7 :Zinterval" from the "TESTS" menu.

Now go to the "TESTS" menu so press ( this screen will appear)

Arrow right to "TEST " . Arrow down to " 7 : ZInterval " ( see below left)

Press (you will see upper right screen)

You must highlight either "Data" or "Stats" and press

If you choose "Data", the calculator will read the data from LIST.
If you choose "Stats", you will have to enter the settings yourself.

For this problem we want to highlight "Stats", and press

Next You must set s : 12, mean : 100, n : 35, C-Level : .95
Now highlight "Calculate" and press (see screen below)

As you can see our confidence interval is ( 96.024 , 103.98 ) This means that repeated samples from this population will give a mean value between 96.024 and 103.98 95% of the time.

Example 2 (using actual Sample Data)

Say we want to report the mean of this simple random sample of 10 { 7 , 7, 8, 9, 7, 10, 6, 8, 9, 9 } using a 0.01 level-of- significance, taken from a known Normal Population of 120 where the population standard deviation is 1.2

For this problem we want a Z-Interval since we have a known sigma.
First we will enter our data into List1. (see screen below)

Next we need to once again go to the TEST menu by pressing

Arrow right to "TEST" and highlight "7 : ZInterval"

Press (upper left screen will appear)

This time we want to choose "Data" So highlight “Data” and press

(When you press ENTER the screen will automatically change to upper right.)

You will need to change the s to 1.2 and the "C-Level" to .99 ,
And make sure the List : L1 (our data is in list1)

Now highlight "Calculate" and press ( you will see this screen)

We can see that the interval estimate using a = .01 is (7.0225 , 8.9775)

Again, this means that with repeated samples we will get a mean value between 7.0225 and 8.9775, 99 % of the time.