### 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.

##