## Hypothesis Testing 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