Objectives (BPS chapter 12) General rules of probability 1. Independence : Two events A and B are independent if the probability that one event occurs is not influenced by the occurrence of the other event. 2. multiplication rule for independent events: P(A and B) = P(A) P(B) 3. The general addition rule: P(A or B) = P(A) + P(B) – P(A and B) 4. Conditional probability: 5. General multiplication rule: P(A and B) = P(A)P(B|A) 6. If A and B are independent, then P(A and B) = P(A)P(B)

Objectives (BPS chapter 13) Binomial distributions 1. The binomial setting: Fixed number of trials, probability of success 2. Binomial distributions B(n, p): models for some categorical variables, typically representing the number of successes in a series of n trials. 3. Binomial probabilities: 4. Binomial mean and standard deviation: 5. The Normal approximation to binomial distributions: If X is the count of successes in the sample and np ≥10 and n(1 − p) ≥10, the sampling distribution for large sample size n is:

Objectives (BPS chapter 14) Confidence intervals: σ known 1. C% Confidence intervals for the mean when population standard deviation,σ known. 2. Choosing the sample size

Objectives (BPS chapter 15) 1. Tests of significance: σ known Step 1: Stating hypotheses H 0 : the statement being tested, a statement of “no effect” or “no difference”. H a : the claim we are trying to find evidence for Step 2: Calculate Test statistics Step 3: Obtain P-values using Table A Step 4: If the P-value is equal to or less than α (p ≤ α), then reject H 0. If the P-value is greater than α (p > α), then fail to reject H Tests from confidence intervals: Because a two-sided test is symmetrical, you can also use a confidence interval to test a two-sided hypothesis.

Objectives (BPS chapter 18) Inference about a Population Mean: σ unknown 1 The one-sample t confidence interval 2. The one-sample t test : 3. Use Matched pairs t test if two samples are not independent H 0 :  difference = 0 ; H a :  difference > 0 (or <0, or ≠0)

Objectives (BPS chapter 19) Comparing two population means: σ 1, σ 2 unknown 1. Degree of freedom, df= smallest (n 1 −1; n 2 −1) 2.Two sample t-confidence interval 3. Two-sample t-test

Objectives (BPS chapter 20) Inference for a population proportion 1. The sample proportion 2. The sampling distribution of 3. Large sample confidence interval for p 4. Choosing the sample size 5. Significance tests for a proportion

Objectives (BPS chapter 21) Comparing two proportions 1. The sampling distribution of a difference between proportions 2. Large Sample confidence intervals for comparing two proportions 3. Significance tests for comparing proportions

Objectives (BPS chapter 23) The chi-square test 1. Chi-square hypothesis test H 0 : There is no relationship between categorical variable A and B. H a : There is some relationship between categorical variable A and B. 2. Expected counts in two-way tables 3. The chi-square test Obtain p-value using Table E with degree of freedom, df=(r-1)(c-1) 4. Cell counts required for the chi-square test  All individual expected counts are 1 or more (≥1)  No more than 20% of expected counts are less than 5 (< 5)

Objectives (BPS chapter 24) Inference for regression 1. Testing the hypothesis of no linear relationship H 0 :  = 0 vs. H a :  ≠ 0, >0, or <0 Find the p-value using Table C with degree of freedom, df=n-2 2. Confidence intervals for the regression slope: 3. prediction interval for a single observation when x=x * : 4 confidence interval for the mean response when x=x * :