Definition

1. Definition • Null Hypothesis: • Statement of no difference • Sometimes based on original idea (not hoped for values) • Claim used to assess the strength of the evidence against the null hypothesis

2. Definition As I am currently reading the excellent book Fisher, Neyman, and the Creation of Classical Statistics by the late Erich L. Lehmann (post- humously published in July 2011), in Chapter 5, titled "The Design of Experiments and Sample Surveys", he quotes and comments on Fisher's groundbreaking 1935 book The Design of Experiments, with the following from a second-chapter section of it titled 'The Null Hypothesis' (on Page 64 of Lehmann's monograph): 'In this case, the hypothesis that the judgments given are in no way influenced by the order in which the ingredients have been added... This hypothesis, which may or may not be impugned by the result of an experiment, is again characteristic of all experimentation. Much confusion would be avoided if it were explicitly formulated when the experiment is designed. In relation to any experiment, we may speak of this hypothesis as the "null hypothesis," and it should be noted that the null hypothesis is never proved or established, but it is possibly disproved, in the course of experimentation.' Lehmann adds: "The paragraph ends with a sentence that has often been quoted: 'Every experiment may be said to exist only in order to give facts a chance of disproving the null hypothesis.'"

3. Definition • P-Value • Probability that our found value could occur randomly assuming the null hypothesis is true • It follows that the smaller the p value the more likely it is the rejection of the null • Based on the idea that it is less likely to randomly occur • Value is found via conditional probability and the assumption of normality • Statistically Significant • If P-value is smaller than alpha, the data are statistically significant at level a • Results in rejection of null hypothesis in favor of alternative hypothesis

4. Example • For his second semester project in AP Statistics, Zenon decided to investigate whether students at his school prefer name-brand chips to generic potato chips. He randomly selected 50 students and had each student try both types of chips, in random order. Overall, 34 of the 50 students preferred the name-brand chips. Zenon performed a significance test using the hypothesis where p=the true proportion of students at his school who prefer name-brand chips. The resulting P-value was .0055. Was this finding significant at the following levels? What occurred for each instance?

5. Example

6. Definition • Power • The power of a test against a specific alternative is the probability that the test will reject H0 at a chosen significance level α when the specified alternative value of the parameter is true. • Power is an indicator of strength of use of the process/statistics that have been developed • To test the probability of a Type II Error, we use the value found from a Type I error and test it against the assumed value. • i.e. we use the value that we’d need to mistakenly reject the null to see the probability that we would reject the null given a specific sample statistic. • Power is close to 0 means that not rejecting is high even though it should be, power close to 1 means that rejecting is likely when it should be • Note: The power of a test against any alternative is 1-the probability of a Type II error for that alternative.

7. In a school that has 20 teachers, 10 teach humanities, 8 teach social studies and 6 teach science. Two teach both humanities and social studies, but none teaches both social studies and science. How many teach both humanities and science?

8. The Pledge I can be the best By doing my best In everything I do And taking pride in who I am My DETERMINATION will see me through Who are we? The mighty, mighty Gryphons! What’s our mission? To succeed in COLLEGE How do we achieve? With good character and unity To make us what? The best in the COUNTRY!

9. No Clickers Bellwork • Eight people walk into a meeting. Not wanting to be rude, each person shakes hands with every other person. How many handshakes occur?

10. No Clickers Bellwork • At a dinner party, each man shook hands with everyone but his spouse, but no women shook hands. If 13 heterosexually married couples attended, how many handshakes occurred among the 26 people?

11. Quiz • In a school that has 24 teachers, 15 teach humanities, 8 teach social studies and 9 teach science. Two teach both humanities and social studies, one teaches all three, but none teach just social studies and science. How many teach both humanities and science?