Warm-up8.3 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 tworolls to get a six the first time? A) B) C) D) E)

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8.3 and 8.4 Confidence Interval and Inference Test for a Difference Between Two Independent Proportions

Same as one proportion, except slightly different formulasand one more condition.

Confidence interval for a population difference in proportions

On Calculator: STAT -> TESTS -> 2 PropZInt.Extra condition: Plausible Independence Condition – It isimportant to be certain the sample groups are independentof each other AND success/failure condition (must be at least 5 ineach category)

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Finding a Confidence IntervalA recent study of 1000 randomly chosen residents in each of tworandomly selected states indicated that the percent of people living inthose states who were born in foreign countries was 6.5% for State Aand 1.7% for State B. Find a 99% confidence interval for the differencebetween 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 HighwayTraffic Safety Administration. Of 4208 male drivers withfemale passengers , 2777 (66.0%) were belted. But among2763 male drivers with male passengers only, 1363 (49.3%)wore seatbelts.Complete a significance test to determine if there is adifference in proportions between male drivers who wearseatbelts when sitting with male passenger and theproportion who wear seatbelts when sitting next tofemale passenger?

Finish the significance TestIndependence

Randomization

Population Sizes

Success/Failure

Because the conditions are satisfied, I’ll use a Normal modeland perform a two-proportion z-test.

Step 2, Step 3, Step 4Step 2 : State the hypotheses. Ho: There is no difference between

the proportion of males wearingseatbelts with female passengers and the proportion ofmales wearing seatbelts with male passengers.HA: There is a difference between the proportion of males

wearing seatbelts with female passengers and the proportionof males wearing seatbelts with male passengers.Step 3 : STAT-> TESTS - > 2-PropZTestWrite z-score (test statistic), p-value, make a pictureStep 4: Write a conclusion.

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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 45Next block Notebook Check10.1, 10.2, 10.3, Ch. 11 Day 1, Ch. 11 Day 2, 8.3&8.4, 9.3 &9.47 notes with warm-ups – must be completed for credit!7 x 14 points = 98 pts