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Chapter 5: Q 9. (page 294)
Due to a hit, A very good professional baseball player gets a hit about of the time over an entire season. After the player failed to hit safely in six straight at-bats, a TV commentator said, “He is due for a hit by the law of averages.” Is that right? Why?
It was not right.
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Lotto In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry
out a simulation to answer this question. Follow the four-step process.
Who eats breakfast? The two-way table describes the 595 students who responded to a school survey about eating breakfast. Suppose we select a student at random. Consider events B: eats breakfast regularly, and : is male.
(a) Find Explain what this value means.
(b) Find Explain what this value means.
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 “No” 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’s sample say “No.” Explain why this result does not give convincing evidence that fewer than half of the school’s students brush their teeth with the water off.
(b) Suppose 18 students in the class’s sample say “No.” Explain why this result gives strong evidence that fewer than 50% of the school’s students brush
their teeth with the water off.
You want to estimate the probability that the player makes or more of shots. You simulate 10 shots 25 times and get the following numbers of hits:
What is your estimate of the probability?
(a) , or (d) , or
(b) , or (e) , or
(c) , or
Crawl before you walk (3.2) At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that
restrict their movement? Perhaps there might even be an association between babies’ crawling age and the average temperature during the month they first try to crawl (around six months after birth). Data were collected from parents who brought their babies to the University of Denver Infant Study Center to participate in one of a number of studies. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. Information was obtained on infants ( boys and girls). Crawling age is given in weeks, and average temperature (in °F) is given for the month that is six months after the birth month. Analyze the relationship between average crawling age and average temperature. What do you conclude about when babies learn to crawl?
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