1. SWBAT: -Determine whether to use a one or two tailed test and calculate the necessary p-value -Make and interpret a decision based on the results of a statistical test -Write a claim for a statistical test Agenda: -Review homework -Notes: power point -Assign homework

2. Statistical Tests and P-Value Comparing a population parameter to sample statistic Population Parameter Test Statistic µ σ2σ2 s2s2 p P – Value (Probability Value) -The smallest level of significance for which the sample statistics tells us to reject H 0

3. There are 3 type of hypothesis tests Left Tail Right Tail Two Tail The type of test depends on the region, indicated by H a, that favors rejecting H 0. H a includes less than symbol, therefore it is a left tail test

4. H a includes greater than symbol, therefore it is a right tail test

5. Example: Determine the Null and Alternative hypothesis for each statement. State if graph is left, right or two tail then sketch and shade area for P-value. A city claims that its unemployment rate is 7.6%

6. A new teaching method claims to improve SOL scores by 20 or more points Example: Determine the Null and Alternative hypothesis for each statement. State if graph is left, right or two tail then sketch and shade area for P-value.

7. Making and Interpreting the Decision To finish a hypothesis test, make one of the following decisions: 1) Reject Null Hypothesis 2) Fail to Reject Null Hypothesis Decision Based on P-Value Compare P-Value and α 1.If P-value ≤ α, then reject H 0 2.If P-Value > α, then fail to reject H 0

8. Claim DecisionsClaim is H 0 Claim is H a Reject H 0 Enough evidence to reject claim Enough evidence to support claim Fail to Reject H 0 Not enough evidence to reject claim Not enough evidence to support claim Interpreting Results

9. Example: For the following example, how would you interpret your decision if you reject H 0 ? If you fail to reject H 0 ? A car maker advertises their new hybrid gets more than 40 mpg. Claim is H a. H 0 : µ ≤ 40 If we reject H 0 then there is enough evidence to support the car makers claim of more than 40 mpg. If we fail to reject H 0 then there is not enough evidence to support the makers claim of more than 40 mpg.

10. Example: For the following example, how would you interpret your decision if you reject H 0 ? If you fail to reject H 0 ? A company advertises that its employees starting salaries are $56,000 or more. Claim is H 0 H 0 : µ ≥ $56,000 If we reject H 0 then there is enough evidence to reject the companies claim that their employees make $56,000 or more If we fail to reject H 0 then there is not enough evidence to reject the companies claims that their employees make $56,000 or more

11. Steps for a Hypothesis Test 1.State H 0 and H a 2.Identify α 3.Determine whether to use z or t distribution, draw graph (will show left, right or two tailed test) 4.Calculate test statistic and corresponding test statistic (z or t score) 5.Find P-Value 6.Compare P-Value and α to make decision 7.Write a conclusion interpreting the decision

12. Strategies for writing H 0 and H a Are you trying to support a claim or reject a claim? If trying to support, you cannot support it if your claim is null hypothesis, so to get a favorable conclusion, write your claim as the alternative hypothesis. If you are trying to reject, then write your claim as the null hypothesis

13. Example: A group of educators is claiming that their new teaching method will improve Algebra 1 SOL scores by more than 20 points. How would you write a null and alternative hypothesis if (1) you were a member of that group and want support for your claim? (2) you are in a group that opposes the other group and want to reject their claim? 1) Since group 1 is trying to support their claim, they would make an alternative hypothesis statement, H a : µ > 20, and then make the null hypothesis the complement, H 0 : µ ≤ 20. 2) Since group 2 is trying to reject group 1’s claim, they would state the null hypothesis, H 0 : µ ≥ 20, and then the alternative hypothesis, Ha: µ <20.

14. Homework Pg 367 #22-52 even