1. Topic 10: Hypothesis Testing
Hypothesis testing for a single proportion
Hypothesis testing for a single mean

2. Hypothesis Testing For a proportion

3. Hypothesis Testing Example
A manufacturer claims that only 2% of the women using the company’s birth control pill suffer from side effects. Recent investigations by several journalists suggest this estimate is too low. We want to test the manufacturers claim.
How would we do that?

4. Hypothesis Testing Example
A manufacturer claims that only 2% of the women using the company’s birth control pill suffer from side effects. Recent investigations by several journalists suggest this estimate is too low. We want to test the manufacturers claim.

5. Calculator 1-PropZTest (proportions, hypothesis testing) p0: .02 x: 23
Select prop > p0
Select Calculate for P-value; Select Draw to see the normal curve and get the P-value

6. Assumptions for a hypothesis test for a population proportion
We have a random sample from the population
The sample is large enough so that we see at least 15 observations of both possible outcomes

7. Hypothesis Testing For a Mean

8. Hypothesis Testing Example
In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4 Celsius was obtained for 61 temperatures recorded on 61 different days, with a standard deviation of 1.7 Celsius. Test the claim that the population mean is 30 Celsius.

9. Calculator Ttest (mean, hypothesis testing) 0: 30 x: 30.4 Sx: 1.7
 ≠ 0

10. Assumptions for a hypothesis test for a population mean
We have a random sample from the population
Either sample size is large (30 or larger) or the population is normally distributed

11. Make a Decision
The P-value is a cutoff: if P-value < α we reject the null hypothesis; otherwise, we fail to reject the null hypothesis. We can also express our conclusion using the table below (ranges can vary depending on the application).
Could we have made an error?

12. Could We Have Made an Error? Yes
Sometimes one is more serious, sometimes the other!