1. Chapter 7 Hypothesis Testing with One Sample Let’s begin…

2. 7.1 Introduction to Hypothesis Testing I.Hypothesis Tests Hypothesis Test: a process that uses sample statistics to test a claim about the value of a population parameter II.Stating a Hypothesis Statistical Hypothesis: a verbal statement, or claim, about a population parameter

3. To test a population parameter, you should state a pair of hypotheses – 1 represents the claim, the other its complement. Either hypothesis may represent the original claim. Null Hypothesis: H o : contains a statement of equality ≤, =, ≥. Alternative Hypothesis: H a : is the complement of the null. It is a statement that must be true if H o is false.

4. TAKE OUT YOUR BOOK! Lets try some….page 334 1) 2) 3)

5. Practice Makes Perfect… Now turn to page 343 9) 23) Classwork to be collected: Page 343 #10, 12, 24, 26 HW: p343 #11, 13, 14, 25, 27, 28

6. III. Types of Error No matter which hypothesis is the claim, you always begin assuming the null is true. So you make one of two decisions: 1. Reject the null hypothesis 2. Fail to reject the null hypothesis (NEVER say accept!) Court discussion…to explain

7. Because your decision is based on a sample rather than the entire pop- ulation, there is always the possibility you will make the wrong decision. Type I Error: occurs if the H o is rejected when it is true. Type II Error: occurs if the H o is not rejected when it is false

8. Lets read Example 2 together on pg 336 (SO open your book now) Try It Yourself 2, p336 Now try independently page 344 #29 HW: p344 #30 – 34 YOU MUST WRITE OUT THE SENTENCES

9. Level of Significance Your maximum allowable probability of making an error. Most commonly used levels are: α = 0.01α = 0.05α = 0.10

10. IV. Statistical Tests and P-values Test Statistic: the statistic that is compared with the parameter in the null hypothesis P-value: a probability…the smaller the p- value the more evidence there is to reject the null hypothesis (rare occurrence)

11. LEFT TAILED TEST: Ha is less than RIGHT TAILED TEST: Ha is greater than TWO TAILED TEST: Ha is not equal to (each tail has an area = 1/2P)

12. OPEN YOUR BOOK TO PAGE 339 Try It Yourself #3 1) 2) DO NOW: p343 #19-22, 35, 37, 39

13. V. Making & Interpreting a Decision Decision Rule based on P-value 1) If P ≤ α then reject the Ho 2) If P > α then fail to reject Ho Failing to reject the null hypothesis does not mean you have accepted it as true. It simply means there is not enough evidence to reject the null.

14. Look at table on page 340! If Ho is the claim use the word reject. If Ha is the claim use the word support. Let’s do example 4 together… Now you do Try it Yourself #4.

15. Steps for Hypothesis Testing 1)State the hypotheses & identify the claim 2)Find the test statistic & sketch a normal curve 3)Find the p-value 4)Compare your p-value to your level of significance and make a decision 5)Write a sentence interpreting your decision in context.

16. VI. Strategies for Hypothesis Testing Your strategy depends on whether you are trying to support or reject your claim… –If support: your claim has to be your alternative hypothesis –If reject: your claim has to be your null hypothesis ***Read example 5 and do TIY#5, please.***

17. PRACTICE Together: page 345 #41, 47 Homework: pg 345 #43, 45, 49 Classwork: pg345 #42 – 50 even