Warm-up 8.3 and 8.4 C.I.and Inference Test of two Ind. Proportions 1. Consider two events: E and F. We know that P(E) = P(F) = 0.7. Are the two events E and F disjoint? A) Yes. B) No, because P(E) and P(F) are equal. C) No, because P(E and F) is unknown. D) No, because P(E) and P(F) add up to more than 1. 2.Suppose Lynn rolls a fair die until a six appears on top. What is the probability that it will take Lynn more than two rolls to get a six the first time? A) B) C) D) E)

H.W P#11, P#13 a - c P.13

13. c.

8.3 and 8.4 Confidence Interval and Inference Test for a Difference Between Two Independent Proportions Same as one proportion, except slightly different formulas and one more condition. Confidence interval for a population difference in proportions On Calculator: STAT -> TESTS -> 2 PropZInt. Extra condition: Plausible Independence Condition – It is important to be certain the sample groups are independent of each other AND success/failure condition (must be at least 5 in each category)

Finding a Confidence Interval A recent study of 1000 randomly chosen residents in each of two randomly selected states indicated that the percent of people living in those states who were born in foreign countries was 6.5% for State A and 1.7% for State B. Find a 99% confidence interval for the difference between the proportions of foreign born residents for these two states.

Significance Test for a Two-sample difference between two proportions Seatbelt was recorded at 161 locations in Masachusettes, using a random-sampling methods by the National Highway Traffic Safety Administration. Of 4208 male drivers with female passengers, 2777 (66.0%) were belted. But among 2763 male drivers with male passengers only, 1363 (49.3%) wore seatbelts. Complete a significance test to determine if there is a difference in proportions between male drivers who wear seatbelts when sitting with male passenger and the proportion who wear seatbelts when sitting next to female passenger?

Finish the significance Test Independence Randomization Population Sizes Success/Failure Because the conditions are satisfied, I’ll use a Normal model and perform a two-proportion z-test.

Step 2, Step 3, Step 4 Step 2 : State the hypotheses. H o : There is no difference between the proportion of males wearing seatbelts with female passengers and the proportion of males wearing seatbelts with male passengers. H A : There is a difference between the proportion of males wearing seatbelts with female passengers and the proportion of males wearing seatbelts with male passengers. Step 3 : STAT-> TESTS - > 2-PropZTest Write z-score (test statistic), p-value, make a picture Step 4: Write a conclusion.

Next two blocks! If you haven’t started reviewing, start reviewing for the cumulative test. Print out the Unit Reviews, go over old tests and quizzes, go to the link for Dr. Tang’s Notes on Sharepoint. Next block bring a printed copy of the practice cumulative test in addition to reading 8.4 and completing D 45 Next block Notebook Check 10.1, 10.2, 10.3, Ch. 11 Day 1, Ch. 11 Day 2, 8.3&8.4, 9.3 &9.4 7 notes with warm-ups – must be completed for credit! 7 x 14 points = 98 pts