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Warm-up 8.3 and 8.4 C.I.and Inference Test of two Ind. Proportions

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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 two

rolls to get a six the first time?

A) B) C)

D) E)

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.

Ho: There is no difference between

the proportion of males wearing

seatbelts with female passengers and the proportion of

males wearing seatbelts with male passengers.

HA: 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

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