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Chapter 5: Q. 99. (page 336)
Checking independence Suppose A and B are two events such that, and. Are events A and B independent? Justify your answer.
Events and are independent
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If a player rolls a , it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?
a.
b.
c.
d.
e.
Lefties A website claims that of U.S. adults are left-handed. A researcher believes that this figure is too low. She decides to test this claim by taking a random sample of U.S. adults and recording how many are left-handed. Four of the adults in the sample are left-handed. Does this result give convincing evidence that the website鈥檚 claim is too low? To find out, we want to perform a simulation to estimate the probability of getting or more left-handed people in a random sample of size from a very large population in which of the people are left-handed.
Let to indicate left-handed and to 99 represent right-handed. Move left to Page Number: right across a row in Table . Each pair of digits represents one person. Keep going until you get different pairs of digits. Record how many people in the simulated sample are left-handed. Repeat this process many, many times. Find the proportion of trials in which or more people in the simulated sample were left-handed.
In a sample ofstudents, say they are vegetarians. Of the vegetarians, eat both fish and eggs, eat eggs but not fish, and eat neither. Choose one of the vegetarians at
random. What is the probability that the chosen student eats fish or eggs?
a.
b.
c.
d.
e.
Double fault!A professional tennis player claims to get of her second serves in. In a recent match, the player missed of her first second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss or more of her first second serves.
a. Describe how to use a random number generator to perform one trial of the simulation. The dot plot displays the number of second serves missed by the player out of the first second serves in simulated matches.
b. Explain what the dot at represents.
c. Use the results of the simulation to estimate the probability that the player would miss or more of her first second serves in a match.
d. Is there convincing evidence that the player misses more than of her second serves? Explain your answer.
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 students at their school if they usually brush with the water off. In the sample, students said "Yes." The dotplot shows the results of taking SRSS of students from a population in which the true proportion who brush with the water off is .
a. Explain why the sample result (of the students said "Yes") does not give convincing evidence that fewer than half of the school's students brush their teeth with the water off.
b. Suppose instead that of the students in the class's sample had said "Yes." Explain why this result would give convincing evidence that fewer than of the school's students brush their teeth with the water off.
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