One sample Z-Tests

Always start each new problem from the home screen

With **all** Hypothesis Testing we will need to develop the null and alternative
hypothesis. We will then test the **alternative** hypothesis (**Ha**) ,

If the "p" value is less than the level of significance (alpha,) we reject Ho.
If the "p" value is greater than or equal to the level of significance then we
can not reject Ho.

In short: ** p < >>>>>>>>>>>>>reject Ho,**

p >>>>>>>>do not reject Ho.

**Example 1 (One Tailed Z-Test)**

New tires manufactured by a company outside Ocala, Fl. , are designed to provide a mean life expectancy of at least 40,000
miles. The tire rating has a standard deviation of 1000 miles. A test with 30 tires shows a sample mean
of 39,600 miles.

Using a 0.02 level of significance, test whether or not there
is sufficient evidence to reject the claim of a mean of at least 40,000 miles.

For this problem a **Z-Test** is appropriate. **(n=30, known s)**

**Ho : 40,000
Ha : < 40,000
**

**so We will reject Ho if p < .02
We can not reject Ho if p .02**

On the calculator we start from the "**TESTS**" menu. Press
(you will see this screen)

**" 1 : Z-Test..."** should be highlighted then press (see screen below)

Now we must highlight either "**Data**" or "**Stats**".

If we want to enter the data ourselves we choose "Stats".

For our problem we highlight "Stats" and press

**Arrow down** and change settings to match this screen. (see screen above)

Highlight "**Calculate**" and press ENTER ( this screen will appear)

We can see from the screen that the "p" value is **0.014** which is less than
**0.02**. So we reject **Ho.**

**Example 2 ( Two Tailed Z-Test )**

A particular bottled beer filling process is designed to fill bottles with a mean
of 12 Fl. Oz. This process has a standard deviation of .07 Fl. Oz.
Quantities over or under this amount are undesirable.

A sample of 10 bottles is taken to determine if the process is within limits.
These are the sample volumes:

**{ 11.6 12.1 11.9 12.8 11.9 12.0 12.4 11.6 11.8 12.3 }**

Using a 0.05 level of significance, test to see if the sample results indicate the filling process is functioning properly.

For this problem: **Ho: = 12 ; Ha : 12**

On the calculator we will first enter the data into LIST1.

Next we will go to the "**TESTS**" menu. So press

**Arrow right** to "**TESTS**"( you will see this screen)

Highlight "**1 : Z Ð Test...**" Press (this screen will appear)

Once again we must choose either "**Data**" or "**Stats**".
This time we will choose "Data". Arrow down and change the settings to fit our problem.

= 12 , = .07 . Recall we always test **Ha**.

Highlight "**Calculate**" and press (you will see this screen)

From the screen we see the "p" value is .071 which is greater than 0.05

Therefore we **can not reject Ho** .