One Tailed T-Test

Always start each new problem from the home screen

A local Flea market business decided to sell their own "Salsa in a jar".
The process of "canning" the salsa is designed to produce a mean of at least 120
jars of salsa per batch. Quantities under this amount are undesirable.
A sample of 10 batches shows the following numbers of jars of salsa:

{ 108 118 120 122 119 113 124 122 120 123 }

Using = 0.05 , test to see if the sample results indicate the "canning"
process is functioning properly.
For this problem we have unknown sigma, and small sample size so we need to use a "T=Test"
For this problem Ho : 120 ;
Ha : < 120, so reject Ho if p < .05

To begin this problem we first enter the sample data into "List1"
Next, on the calculator go to the "**TESTS**" menu.
Press

**Arrow right** to "**TESTS**" next Arrow down to "**2 : T-Test...**"

Press (you will see this screen)

Once again we must choose between "**Data**" and "**Stats**".
We will choose "Data" for this problem because we have entered the actual data into **list1. Change the other settings on
your calculator to match the screen above.**
Recall we always test Ha so make sure you highlight the appropriate choice,
" < o"

Press **Arrow down** to highlight "**Calculate**". Press

( you will see this screen)

You can see from the screen that the p-value is .24, which is not less than .05. Therefore we can not reject Ho.

Our conclusion would be: There is not sufficient evidence at the alpha=.05 level to reject the claim that the mean number of jars produced
is at least 120.

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

Consider the following hypothesis test:

Ho : = 20

Ha : 20 .

Data from a sample of 10 items gave the following results:

Sample mean = 21.02, s = 1.65.

At what level of would you reject Ho?

A **T-Test** is needed in this situation since we have a small sample with
unknown population distribution and unknown population s.
Remember we reject Ho if p < . We need to determine the p-value for this problem and
then we will have our answer. If alpha is greater than our p-value then we would reject Ho.

On the calculator go to the "**Tests**" menu. **Arrow right** to "**TESTS**" and down
to "**2 : T Ð Test...**" Press ( see screen below)

Match previous settings on your calculator.

Arrow down to "**Calculate**" and press (this screen will appear)

We can see that the p-value at which we would reject **Ho** is .082 .

This means that if alpha were greater than .082 ,( > p), we would reject **Ho**