Hershey’s Kisses and Confidence Intervals (2A)

1. Hershey’s Kisses and Confidence Intervals (2A)

2. Hershey’s Kisses and Confidence Intervals (3A)

3. Hershey’s Kisses and Confidence Intervals (2B)

4. Hershey’s Kisses and Confidence Intervals (3B)

5. Statistical Inference Tests of Significance

6. Statistical Inference • Two most common types: • Confidence Intervals – Use when goal is to estimate a population parameter. • Tests of Significance – Use when goal is to assess the evidence provided by data about some claim concerning a population.

7. Shooting Free Throws • I claim that I have a better free throw percentage than J.J. Redick (.938). To test my claim, you ask me to shoot 20 free throws in the Jordan gym. I make only 1 out of the 20. “Aha!” you say. “Someone who makes more than 93% of her free throws would almost never make only 1 out of 20. So I don’t believe your claim.”

8. Test of Significance • Procedure for comparing observed data with a stated hypothesis. • Basic idea: an outcome that would rarely happen if a claim were true is good evidence that the claim is not true.

9. Hypotheses • Hypothesis: statement about the parameters in a population • Null hypothesis (H0): the statement being tested (usually is a statement of “no effect” or “no difference” • Alternative hypothesis (Ha):the statement we suspect is true instead of H0

10. Hypotheses • The alternative hypothesis is: • one-sided if we are interested only in deviations from the null hypothesis in one direction • two-sided if the direction of the difference between the null and alternative hypotheses is not specified

11. P-value • The probability, computed assuming H0 is true, that the observed outcome would take a value as extreme or more extreme than that actually observed is called the P-value of the test. • The smaller the P-value, the stronger the evidence against H0 provided by the data.

12. Significance Level • We can compare the P-value with a fixed value, called the significance level () • If the P-value is as small or smaller than alpha, we say that the data are statistically significant at level  • “If the P-value’s low, reject the H0”

13. Inference Toolbox: Significance Tests • Identify the population of interest and the parameter you want to draw conclusions about. State null and alternative hypotheses in words and symbols. • Choose the appropriate inference procedure. Verify the conditions for using the selected procedure. • If the conditions are met, carry out the inference procedure. • Calculate the test statistic. • Find the P-value. • Interpret your results in the context of the problem.

14. Globe Toss • The ocean covers 71 percent of the Earth's surface and contains 97 percent of the planet's water. (Source: http://www.noaa.gov/ocean.html) • Let H0: p-hat=.7 • What alternative hypothesis would we like to test?

15. Connection to Confidence Intervals • A level  two-sided significance test rejects a hypothesis H0:μ=μ0 exactly when the value μ0 falls outside a level 1- confidence interval for μ.