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Chapter 5: Q 4.2. (page 323)
Government data show that of adults are full-time college students and that of adults are age or older. Since can we conclude that about of adults are college students or older? Why or why not?
Yes, because the events are independent events.
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Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is lying when they鈥檙e actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test says that the suspect is being truthful when the person is actually lying (a 鈥渇alse negative鈥�). For one brand of polygraph machine, the probability of a false positive is .
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.
Ten percent of U.S. households contain or more people. You want to simulate choosing a household at random and recording whether or not it contains or
more people. Which of these are correct assignments of digits for this simulation? (a) Odd = Yes (or more people); Even = No (not or more people)
(b) = Yes; = No
(c) = Yes; = No
(d) All three are correct.
(e) Choices (b) and (c) are correct, but (a) is not.
Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many
students in the sample would need to say 鈥淣o鈥� to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the
water off is 0.50.
(a) Suppose 27 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result does not give convincing evidence that fewer than half of the school鈥檚 students brush their teeth with the water off.
(b) Suppose 18 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result gives strong evidence that fewer than 50% of the school鈥檚 students brush
their teeth with the water off.
Color-blind men Aboutof men in the United States have some form of red-green color blindness. Suppose we randomly select one U.S. adult male at a time until we find one who is red-green color-blind. How many men would we expect to choose, on average? Design and carry out a simulation to answer this question. Follow the four-step process.
An unenlightened gambler
(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets
heavily on black at the next spin. Asked why he explains that black is 鈥渄ue by the law of averages.鈥� Explain to the gambler what is wrong with this reasoning.
(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
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