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a course in statistics with r

Mind On Statistics 5th Edition Jessica M Utts, Robert F Heckard - Solutions

In Example 7.19(p. 236), we found the probability that both of two unrelated strangers share your birth month. In this exercise, we find the probability that at least one of the two strangers shares your birth month. Assume that all 12 months are equally likely.a. What is the probability that the
In each situation, explain whether the selection is made with replacement or without replacement.a. The two football teams selected to play in the Rose Bowl in a given year.b. The cars stopped by the police for speeding in five consecutive mornings on the same stretch of highway.c. The winning
In each situation, explain whether the selection is made with replacement or without replacement.a. The three digits in the lottery in Example 7.2(p. 225).b. The three students selected to answer questions in Case Study 7.1(p. 222).c. Five people selected for extra security screening while boarding
In Exercise 7.34 it was noted that women between the ages of 40 and 44 have only a 37% chance of being able to bear a child. Joan, Janice and Jennifer are friends, all are in the 40 to 44 age group, and all are trying to have a child. Assume they are representative of a random sample of women in
A high school in a small town always has its homecoming day and parade on the first Saturday in October. From historical records, it has been determined that the probability of rain during the parade is .15. Anna will attend the high school for the next four years and plans to play in the marching
In a recent election, 55% of the voters were Republicans, and 45% were not. Of the Republicans, 80% voted for Candidate X, and of the non-Republicans, 10% voted for Candidate X.Consider a randomly selected voter. Define:A Voter is Republican.B Voted for Candidate X.a. Write values for P(A),
Julie is taking English and history. Suppose that at the outset of the term, her probabilities for getting As are:P(grade of A in English class) .70.P(grade of A in history class) .60.P(grade of A in both English and history classes) .50.a. Are the events “grade of A in English class” and
Refer to Exercise 7.45. Find the following probabilities:a. P(A)b. P(B)c. P(A and B)d. P(A or B)e. P(A and C)f. P(A or C)
A popular lottery game is one in which three digits from 0 to 9 are chosen, so the winning number can be any of the 1000 numbers from 000 to 999. Define:A the first digit is odd B the first digit is even C the second digit is odda. State two of these events that are mutually exclusive.b.
Refer to Exercise 7.43. Now suppose you meet two new friends independently, and ask each of them on what day of the week they were born.a. What is the probability that the first friend was born on a Friday?b. What is the probability that both friends were born on a Friday?c. What is the probability
Suppose that people are equally likely to have been born on any day of the week. You meet a new friend, and ask her on what day of the week she was born.a. List the simple events in the sample space.b. What is the probability that she was born on a weekend(Saturday or Sunday)?
Two fair coins are tossed. Define:A Getting a head on the first coin B Getting a head on the second coin A and B Getting a head on both the first and second coins A or B Getting a head on the first coin, or the second coin, or both coinsa. Find P(A) the probability of A.b. Find P(B) the
A brand of cereal contains a prize in each box. There are five possible prizes, and each of the prizes is equally likely to be in any box.a. If you purchase two boxes, what is the probability that you receive the same prize in both boxes?b. If you purchase two boxes, what is the probability that
Two students each use a random number generator to pick an integer between 1 and 7.a. What is the probability that they pick the same number?b. What is the probability that they pick different numbers?
A fair coin is tossed three times. The event “A getting all heads” has probability 1/8.a. Describe in words what the event AC is.b. What is the probability of AC?
Two fair dice are rolled. The event “A getting the same number on both dice” has probability 1/6.a. Describe in words what the event AC is.b. What is the probability of AC?
Refer to Case Study 7.1. Define C1, C2, and C3 to be the events that Alicia is called on to answer questions 1, 2, and 3, respectively.a. Based on the physical situation used to select students, what is the (unconditional) probability of each of these events? Explain.b. What is the conditional
Refer to Exercise 7.34. Which method of finding probabilities do you think was used to find the “90 percent chance”and “37 percent chance”? Explain.
Refer to Exercise 7.34. Suppose that an American woman is randomly selected. Are her age and her fertility status independent?Explain.
According to Krantz (1992, p. 102), “[In America] women between the ages of 20 and 24 have a 90 percent chance of being fertile while women between 40 and 44 have only a 37 percent chance of bearing children [i.e., being fertile].”Define appropriate events, and write these statements as
Refer to Exercise 7.32. Suppose that a student is asked to choose a number from 1 to 10. Define event A to be that the student chooses the number 5, and event B to be that the student chooses an even number.a. What is P(A and B)?b. Are events A and B independent? Explain how you know.c. Are events
When 190 students were asked to pick a number from 1 to 10, the number of students selecting each number were as follows:Number 1 2 3 4 5 6 7 8 9 10 Total Frequency 2 9 22 21 18 23 56 19 14 6 190a. What is the approximate probability that someone asked to pick a number from 1 to 10 will pick the
Use the information given in Case Study7.1 and the “physical assumption” method of assigning probabilities to argue that on any given day, the probability that Alicia has to answer one of the three questions is 3/50.
Refer to Exercise 7.29, in which a red die and a green die are each tossed once. Explain whether the following pairs of events are mutually exclusive, independent, both, or neither:a. A red die and green die sum to 4; B red die is a 3.b. A red die and green die sum to 4; B red die is a 4.
When a fair die is tossed, each of the six sides (numbers 1 to 6) is equally likely to land face up. Two fair dice, one red and one green, are tossed. Explain whether the following pairs of events are mutually exclusive, independent, both, or neither:a. A red die is a 3; B red die is a 6.b. A
Jill and Laura have lunch together. They flip a coin to decide who pays for lunch and then flip a coin again to decide who pays the tip. Define a possible outcome to be who pays for lunch and who pays the tip, in order—for example, “Jill, Jill.”a. List the simple events in the sample space.b.
Refer to Example7.10(p. 230), in which you and your friend Vanessa enter a drawing for a free lunch in Week 1 and again in Week 2. Events defined were A you win in Week 1, B Vanessa wins in Week 1, C Vanessa wins in Week 2.a. Are events B and C independent? Explain.b. Suppose that after Week
Suppose that events A and B are mutually exclusive with P(A) 1/2 and P(B) 1/3.a. Are A and B independent events? Explain how you know.b. Are A and B complementary events? Explain how you know.General Section Exercises
Suppose that A, B, and C are all disjoint possible outcomes for the same random circumstance. Explain whether each of the following sets of probabilities is possible.a. P(A) 1/3, P(B) 1/3, P(C) 1/3.b. P(A) 1/2, P(B) 1/2, P(C) 1/4.c. P(A) 1/4, P(B) 1/4, P(C) 1/4.
A penny and a nickel are each tossed once. Explain whether the outcomes for the two coins are:a. Independent events.b. Complementary events.c. Mutually exclusive events.
Remember that the event AC is the complement of the event A.a. Are A and AC mutually exclusive? Explain.b. Are A and AC independent? Explain.
Refer to Exercise7.21 in which the number of days a randomly selected student exercised in the previous week is recorded. List the simple events that make up each of these events:a. The student exercised on at least 5 days.b. The student exercised on at most 2 days.c. The student did not exercise
Suppose that we randomly select a student and record how many days in the previous week the student exercised for at least half an hour. Make a list of the simple events in the sample space.
A student wants to send a bouquet of roses to her mother for Mother’s Day. She can afford to buy only two types of roses and decides to randomly pick two different varieties from the following four choices: Blue Bell, Yellow Success, Sahara, and Aphrodite. Label these varieties B, Y, S, A.a. Make
Refer to Example7.5(p. 226). What is the probability that a randomly selected child who slept in darkness would develop some degree of myopia?
Every day, John buys a lottery ticket with the number 777 for the lottery described in Example 7.2. He has played 999 times and has never won. He reasons that since tomorrow will be his 1000th time and the probability of winning is 1/1000, he will have to win tomorrow. Explain whether John’s
Alicia’s statistics class meets 50 times during the semester, and each time it meets, the probability that she will be called on to answer the first question is 1/50. Does this mean that Alicia will be called on to answer the first question exactly once during the semester? Explain.
Give an example of a situation for which a probability statement makes sense but for which the relative frequency interpretation could not apply, such as the probability given by Carl Sagan for an asteroid hitting Earth.
A computer solitaire game uses a standard 52-card deck and randomly shuffles the cards for play. Theoretically, it should be possible to find optimal strategies for playing and then to compute the probability of winning based on the best strategy. Not only would this be an extremely complicated
Casino games often use a fair die that has six sides with 1 to 6 dots on them. When the die is tossed or rolled, each of the six sides is equally likely to land face-up. Using the physical assumption that the die is fair, de termine the probability of each of the following outcomes for the number
Refer to Exercise 7.5. Suppose that Robin wants to find the probability associated with the outcomes in the random circumstances contained in the story. Identify one of the circumstances, and explain how she could determine the probabilities associated with its outcomes.
Explain which interpretation of probability (relative frequency or personal) applies to each of these statements and how you think the probability was determined.a. According to Krantz (1992, p. 161), the probability that a randomly selected American will be injured by lightning in a given year is
applies.a. If a spoon is tossed 10,000 times and lands with the rounded head face up 3000 of those times, we would say that the probability of the rounded head landing face up for that spoon is about .30.b. In a debate with you, a friend says that she thinks there is a 50:50 chance that God
Which interpretation of probability (relative frequency or personal) applies to each of the following situations? If it’s the relative frequency interpretation, explain which of the methods listed in the “In Summary” box at the end of Section
A car dealer has noticed that 1 out of 25 new-car buyers returns the car for warranty work within the first month.a. Write a sentence expressing this fact as a proportion.b. Write a sentence expressing this fact as a percent.c. Write a sentence expressing this fact as a probability.
Suppose that you live in a city that has 125,000 households and a polling organization randomly selects 1000 of them to contact for a survey. What is the probability that your household will be selected?
Is each of the following values a legitimate probability value?Explain any “no” answers.a. .50b. .00c. 1.00d. 1.25e. 2.25
Give an example of a random circumstance in which:a. The outcome is not determined until we observe it.b. The outcome is already determined, but our knowledge of it is uncertain.Section 7.2 Skillbuilder Exercises
Answer Thought Question7.2 on page 223.
Identify three random circumstances in the following story, and give the possible outcomes for each of them:It was Robin’s birthday and she knew she was going to have a good day. She was driving to work, and when she turned on the radio, her favorite song was playing. Besides, the traffic light
Find information on a random circumstance in the news.Identify the circumstance and possible outcomes, and assign probabilities to the outcomes. Explain how you determined the probabilities.
Jan is a member of a class with 20 students that meets daily.Each day for a week (Monday to Friday), a student in Jan’s class is randomly selected to explain how to solve a homework problem. Once a student has been selected, he or she is not selected again that week. If Jan was not one of the
Answer Thought Question7.1 on page 223.
According to a U.S. Department of Transportation website(http://www.bts.gov/press_releases/2010/dot045_10/html/dot045_10.html), 78.7% of domestic flights flown by the top 18 U.S. airlines in January 2010 arrived on time.Represent this in terms of a random circumstance and an associated probability.
In an experiment done at an English university, 64 students held their hands in ice water for as long as they could while repeating a swear word of their choice. The same students also held their hands in ice water for as long as they could while repeating a neutral word. For each condition, the
Refer to the observational study described in Case Study 6.1(p. 195). In the study, a link was found between tooth decay and exposure to lead for 24,901 children. Give an example of a possible confounding variable in addition to those described in the text. Explain why it could be a confounding
Explain why confounding variables are more of a problem in observational studies than in randomized experiments.Give an example.
Refer to Exercise 6.27, in which three randomized experiments are described. In each case, explain the extent to which you think the results from the sample in the experiment could be extended to a larger population.
Explain whether a variable can be:a. Both a confounding variable and a lurking variable.b. Both a response variable and a confounding variable.c. Both an explanatory variable and a dependent variable.
Give an example of an observational study, and explain the difference between a confounding variable and a lurking variable in the context of your example.
Refer to Example6.7(p. 210), “Dull Rats,” which was done by using a completely randomized design.a. What were the treatments in this experiment?b. Were the experimental units the 60 individual rats or the 12 individual experimenters? Explain.c. Explain how the experiment could have been done
(p. 209), illustrating the interaction in this study.c. Write a few sentences that would be understood by someone with no training in statistics explaining the concept of interaction in this study.
A study was done (fictional) to compare the proportion of children who developed myopia after sleeping with and without a nightlight. The study found that the results differed based on whether at least one parent suffered from myopia by age 20. The percents of children suffering from myopia were as
Explain whether it is possible for a variable to be both a confounding variable and an interacting variable.
Refer to Case Study 1.6, in which physicians were randomly assigned to take aspirin or a placebo, and heart attack rates were compared. Draw a figure similar to one of Figures 6.2 through6.7 that illustrates the steps for Case Study 1.6.
Refer to the study in Example6.9 that compares ages at death for left-handed and right-handed people. Draw a figure similar to one of Figures6.2 through6.7 that illustrates the steps for Example 6.9.
Refer to Exercise 6.81 and answer these questions.a. For each study, on the basis of the information given, is it clearly a randomized experiment? If not, explain what additional information would make it clear that the study was a randomized experiment rather than an observational study.b. For
Specify what an individual “unit” is in each of the following studies. Then specify what two variables were measured on each unit.a. A study found that tomato plants raised in full sunlight produced more tomatoes than did tomato plants raised in partial shade.b. A study found that gas mileage
Find an example of a randomized experiment in the news.Answer the following questions about it. Be sure to include the news article with your response.a. What are the explanatory and response variables? What relationship was found, if any?b. What treatments were assigned? Was a control group or
Is it possible for each of the following to be used in the same study (on the same units)? Explain or give an example of such a study.a. A placebo and a double-blind procedure.b. A matched-pair design and a retrospective study.c. A case–control study and random assignment of treatments.
Find an example of an observational study in the news.Answer the following questions about it. Be sure to include the news article with your response.a. What are the explanatory and response variables, or is this distinction not possible?b. Briefly describe how the study was done. For instance, was
Refer to Case Study 6.2(p. 197), “Kids and Weight Lifting.”Did the experiment described there use a completely randomized design, a matched-pair design, or a randomized block design? Explain.
do you think is most likely to be a problem in this research?Explain.
Refer to the study reported in Example 2.2, relating the use of nightlights in childhood and the incidence of subsequent myopia.a. Was the research based on an observational study or a randomized experiment? Explain.b. Which one of the “difficulties and disasters” in Section
In this chapter, you learned that cause and effect can be concluded from randomized experiments but generally not from observational studies. Why don’t researchers simply conduct all studies as randomized experiments rather than observational studies?
in which children were randomly assigned to three treatment groups. Suppose now that 60 children will be randomly assigned to these three groups.Describe how you could carry out the random assignments.
The article also reported that “contrary to popular belief men’s self-esteem may take a greater licking than women’s when their hair just won’t behave. Men were likely to feel less smart and less capable when their hair stuck out, was badly cut or otherwise mussed.” In the context of this
Discuss each of the following “difficulties and disasters” in the context of this research.a. Ecological validity.b. Extending results inappropriately.c. Experimenter effect.
Discuss whether this study could have been blind or doubleblind, and whether you think it was blind or double-blind.
What were the explanatory and response variables for this study? Were they categorical variables or quantitative variables?
Was this an observational study or a randomized experiment?Explain.
refer to a study described in a Sacramento Bee article titled “Much Ado Over Those Bad Hairdos”(January 26, 2000, p. A21). Here is part of the article:Researchers surveyed 60 men and 60 women from 17 to 30, most of them Yale students. They were separated into three groups. One group was
is represented by this statement? Explain.Exercises 6.69 to
Another drawback of the study quoted in the Sacramento Bee was that “people who develop breast cancer are much more likely to remember whether they took hormones compared to women who don’t develop the disease.” Which of the “difficulties and disasters” in Section
is represented by this statement?Explain.
One drawback of the study quoted in the Sacramento Bee was that “the women in the study may not resemble women today, because many women now take lower doses of pro gestin than was used during the follow-up years of the study (1979–95).” Which of the “difficulties and disasters” in Section
Assuming that the women and their physicians made the decision about which treatment to pursue (combined hormones, estrogen alone, or no hormones), discuss the possibility of confounding variables in this study.
Near the end of the Sacramento Bee article, it was noted that “the NCI researchers analyzed their results by the woman’s weight. . . There was no increased breast cancer risk in heavier women.” Which of the “Difficulties and Disasters” in Section 6.4 is represented by this
To whom are the women taking combined therapy and estrogen alone being compared when the increased risks of 8%and 1% are computed?
What are the explanatory and response variables for this study? Are they quantitative or categorical? If they are categorical, what are the categories?
Discuss whether this research is the following:a. A case–control study.b. A retrospective study or a prospective study.
Do you think this research was an observational study or a randomized experiment? Explain.
Pick the two “difficulties and disasters” that are most likely to be a problem in each of the following studies, and explain why they would be a problem.a. To compare marketing methods, a marketing professor randomly divides a large class into three groups and randomly assigns each group to
A categorical interacting variable defines subgroups for which the effect of the explanatory variable on the response variable differs. For instance, as explained in the text, for the nicotine patch experiment described in Case Study 6.3, one interacting variable was whether or not there were other
Refer to Exercise 6.57, describing a case–control study relating childhood diet and heart disease. Comment on the extent to which each of the following is likely to be a problem.a. Confounding variables and the implication of causation in observational studies.b. Extending results
Pick the two “difficulties and disasters” that are most likely to be a problem in the following study, and explain why each would be a problem: A researcher at a large medical clinic wants to determine whether a high-fat diet in childhood is more likely to result in heart disease in later life.
Is the experimenter effect most likely to be a problem in a study that is double-blind, single-blind, or not blind at all? Explain.
Refer to Exercise 6.27, in which three randomized experiments are described. For each of the experiments described, pick one of the “difficulties and disasters” described in Section 6.4, and explain how it might be a problem in that experiment.
Refer to Exercise 6.41, describing a study about pet ownership and marriage. Explain whether each of the following is likely to be a problem for that study:a. Confounding variables and the implication of causation in observational studies.b. The Hawthorne effect and experimenter effects.c. Lack of
A retrospective study of 517 veterans who never smoked was done to determine whether there was an association between lung disease and exposure to workplace gases, dust, and fumes (Clawson, Stanford Report, November 1, 2000).In this study, subjects were asked whether or not they remembered being

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