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Chapter 5: Q 69. (page 329)

Sampling senators Refer to Exercise 67. Are events D and F independent? Justify your answer.

Short Answer

Expert verified

Yes, not independent.

Step by step solution

01

Step 1. Given Information

The two-way table shows who lives and who dies among adult passengers. Consider the fact thatD is a democrat, R is a republican, andF is a female.

02

Step 2. Concept Used

P(A/B)=P(AandB)P(B)

The number of favorable outcomes divided by the total number of possible outcomes equals probability. As a result, the following is a definition of conditional probability:

03

Step 3. Calculation

P(D|F)=1317≈0.7647

P(D)=60100≈0.6

There should be no difference in likelihood because D and F are unrelated.

As a result, they are not self-sufficient.

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Most popular questions from this chapter

If I toss a fair coin five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is (a) 0.5. (b) less than 0.5 (c) greater than 0.5 (d) 0 (e) 1 Exercises 33 to 35 refer to the following setting. A basketball player makes 47% of her shots from the field during the season.

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent survey, 50% of people aged 13 and older in the United States are addicted to email. To simulate choosing a random sample of

20people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a

time. A red card means that person is addicted to email; a black card means he isn’t. Continue until you have drawn 20cards (without replacement) for the sample.

(b) A tennis player gets 95%of his second serves in play during practice (that is, the ball doesn’t go out of bounds). To simulate the player hitting 5second serves, look at pairs of digits going across a row in Table D. If the number is between 00and 94, the service is in; numbers between 95and 99indicate that the service is out.

Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say “Yes” to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.

(a) Suppose 55 students in the class’s sample say “Yes.” Explain why this result does not give convincing evidence that more than half of the school’s students recycle.

(b) Suppose 63 students in the class’s sample say “Yes.” Explain why this result gives strong evidence that a majority of the school’s students recycle.

Who eats breakfast? Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, “Do you eat breakfast on a regular basis?” All 595 students in the school responded to the survey. The resulting data are shown in the two-way table

below.7 Male Female Total Eats breakfast regularly 190110300 Doesn’t eat breakfast regularly 130165295Total320275595

(a) Who are the individuals? What variables are being measured?

(b) If we select a student from the school at random, what is the probability that we choose

  • a female?
  • someone who eats breakfast regularly?
  • a female who eats breakfast regularly?
  • a female or someone who eats breakfast

regularly?

Nickels falling over You may feel it’s obvious that the probability of a head tossing a coin is about12because the coin has two faces. Such opinions are not always correct. Stand a nickel on the edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over. Do this 25time, and record the results.

(a) What’s your estimate for the probability that the

coin falls heads up? Why?

(b) Explain how you could get an even better estimate.
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