Section 9-4

Hypothesis Testing Means

This formula is used when the population standard deviation is known.

Once you have the test statistic, the process is the same as it was in section 9.2 and 9.3.

This formula is used when the population standard deviation is unknown. These problems will give you the sample standard deviation. Notice the formula is set up the same way. With this formula you will use a new chart because this is a t-test instead of a z-test.

To determine if you reject or fail to reject the null using the z-test - The process remains the same except

you are using the new formula.

Finding the P-value for the z-test - The process remains the same except

you are using the new formula.

To determine whether you reject of fail to reject using the t-test

Step 1: Find the test statisticStep 2: Find the critical value

- Locate the alpha value- Locate the degrees of freedom- Determine the critical value

Step 3: Compare the test statistic with the critical value

Make sure you follow the decision rules

Test Statistic -

Critical Value – alpha = .05 - degrees of freedom = 15 - two tailed - critical value = 2.131

Decision rule – reject the null if

Conclusion – since 0.5 is less than the critical value we will fail to reject the null, meaning there is not sufficient evidence to support the claim.

To determine the interval of the P-value for the t-test- Step 1 – Find the test statistic using the formula for

the t-test- Step 2 – Find degrees of freedom (this is the sample

size minus one)- Step 3 – Find the two values that the test statistic

falls between.- Step 4 – Look at the top of the chart at the one

tailed or two tailed section depending on the situation, and identify the alphas that go with the two values from step 3.

- Step 5 – Write the two alpha values as an interval.

Test statistic:

Degrees of Freedom = 4

Values from Chart = since this value is less than the lowest value we use the alpha for this number and the second alpha will be 0.5

The two alphas will be 0.1 and 0.5. This will be written as (0.1,0.5)

Test Statistic =

Degrees of Freedom = 60

Two Values = less than -2.660

Alphas = 0.005 and 0

Interval (0,0.005)