1. Testing Hypothesis with Large Samples Classic P – values –(and the calculator, maybe)

2. Classic 1.Make sure the claim is statistical, specific, measurable, and comparable to some benchmark \ 2.Write the null H 0 and alternative H 1 hypothesis. 3.Calculate the test statistic 4.Determine the critical region: two tailed, right- tailed, or left-tailed 5.Determine critical value 6.Is the test statistic in the critical region? Reject H 0. 7.Otherwise, fail to reject (“accept”) 8.Restate the findings vis-à-vis the original claim

3. Testing a Hypothesis The average score on the Algebra 2 midterm is 80. –The mean of 56 scores in my class was a 78, the standard deviation was 12.5 The average SAT score for all statistic students is at least 550. –The mean of 32 students in Middletown was a 540, the standard deviation was 70 The average GPA score for all seniors is more than 2.5. –The mean of 36 students was a 2.7, the standard deviation was 0.8

4. Worksheet Sample mean =n =s = Original claimLabel null and alternative hypothesis Opposite claim Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value Reject or accept?

5. Worksheet Sample mean =n =s = Original claimLabel null and alternative hypothesis Opposite claim Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value Reject or accept?

6. Worksheet Sample mean =n =s = Original claimLabel null and alternative hypothesis Opposite claim Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value Reject or accept?

7. Your Turn The mean body temperature is 98.6 –The mean of 96 temperatures was 99.2, the standard deviation was 0.85 The Mets average more than 81 wins per season –In 49 seasons, the Mets have averaged 76.2 wins (s = 15.8)

8. Worksheet Sample mean =n =s = Original claimLabel null and alternative hypothesis Opposite claim Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value Reject or accept?

9. Worksheet Sample mean =n =s = Original claimLabel null and alternative hypothesis Opposite claim Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value Reject or accept?

10. Homework: Test the claims An inventor claims that his engine will run continuously for 5 hours on a gallon of regular gas. 50 engines are tested. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Use a 95% Degree of Confidence Let’s claim that only children have an average cholesterol level that’s lower than the national average of 190. We test 100 only children and find that x-bar = 198 and s = 15. Use a 99% degree of confidence The national average SAT score is 1000. One high school claims their students are above average. A counselor chooses 30 students and found their average SAT score was 1120 and their standard was 20. Use a 90% degree of confidence

11. More Homework; Test the claims The claim is that the average age of a commercial airliner is at most 18 year. A sample of 85 jets has a mean age of 15.8 years and a standard deviation of 8.3 The car manufacturer claims its fleet of cars averages at least 27 MPG. A sample of 48 cars shows a mean of 78.9 and a standard deviation of 4.1

12. Finding the P value The area is found in by using the test statistic as the z score in table A2 P-value is then calculated as follows –Left tailed: If test statistic < 0then p-value = 0.50 – area else p-value = 0.50 + area –Right tailed: If test statistic < 0then p-value = 0.50 + area else p-value = 0.50 – area –Two tailed: p-value = 2(0.50 – area )

13. Evaluating the p-value If the p-value is less than or equal to the significance level (α), reject the null hypothesis, Otherwise “fail to reject” it.

14. Testing a Hypothesis Claim: the average score on the Algebra 2 midterm is exactly a B The mean of 56 scores in my class was a 78, the standard deviation was 12.5

15. Your turn Claim: South’s mean math SATs are above 570 Data: 100 students, mean SAT is 560, standard deviation is 35

16. Using the Calculator [STAT] TESTS 1: Z-Test… –μ 0 is the benchmark. –σ is the standard deviation –X is the mean –n is the sample size –μ select the format of H 1