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mathematics
statistics
Seeing Through Statistics 4th Edition Jessica M.Utts - Solutions
Refer to the previous exercise about hangover symptoms. Use the Minitab output at the top of the page for this exercise. a. Show how the expected count of 343.27 for the “Male, # 11” category was computed. b. Give the value of the chi-square statistic and the p-value, and make a conclusion.
Refer to Table 8 on page 37 of Original Source 5 on the companion website. Notice that there is a footnote to the table that reads: “p,. 05 and p,. 01, based on chi-square test of association with sex.” The footnote applies to “Grooming**” and “External distraction*.” a. Explain what
The figure at the top of the next page provides Minitab output for testing for a relationship between sex and External distraction, but the expected counts have been removed for you to fill in.a. Fill in the expected counts.b. State the null and alternative hypotheses
Refer to the previous exercise and the accompanying table, categorizing people by sex and whether they were conversing. a. State the null and alternative hypotheses that can be tested with this table. b. Compute the chi-square statistic. c. Make a conclusion in statistical terms and in the context
Suppose a relationship between two variables is found to be statistically significant. Explain whether each of the following is true in that case: a. There is definitely a relationship between the two variables in the sample. b. There is definitely a relationship between the two variables in the
For each of the following possible conclusions, state whether it would follow when the p-value is less than 0.05 (assuming a level of 0.05 is desired for the test). a. Reject the null hypothesis. b. Reject the alternative hypothesis. c. Accept the null hypothesis. d. Accept the alternative
For each of the following possible conclusions, state whether it would follow when the p-value is greater than 0.05 (assuming a level of 0.05 is desired for the test). a. Reject the null hypothesis. b. Reject the alternative hypothesis. c. Accept the null hypothesis. d. Accept the alternative
For each of the following situations, would a chi-square test based on a 232 table using a level of 0.05 be statistically significant? Justify your answer. a. chi-square statistic = 1.42 b. chi-square statistic = 14.2 c. p-value = 0.02
Carefully collect data cross-classified by two categorical variables for which you are interested in determining whether there is a relationship. Do not get the data from a book, website, or journal; collect it yourself. Be sure to get counts of at least five in each cell and be sure the
Find a journal article that uses a chi-square test based on a contingency table. a. State the hypotheses being tested. b. Write the contingency table. c. Give the value of the chi-square statistic and the p-value as reported in the article. d. Write a paragraph or more (as needed) explaining what
Recall that there are two interpretations of probability: relative frequency and personal probability. a. Which interpretation applies to this statement: “The probability that I will get the flu this winter is 30%”? Explain. b. Which interpretation applies to this statement: “The
Use the probability rules in this chapter to solve each of the following: a. According to the U.S. Census Bureau, in 2012, the probability that a randomly selected child in the United States was living with his or her mother as the sole parent was .244 and with his or her father as the sole parent
Figure 9.1 (page 183) illustrates that 17.8% of Caucasian girls have green eyes and 16.9% of them have hazel eyes.In Figurea. What is the probability that a randomly selected Caucasian girl will have green eyes? b. What is the probability that a randomly selected Caucasian girl will have hazel
There is something wrong in each of the following statements. Explain what is wrong. a. The probability that a randomly selected driver will be wearing a seat belt is .75, whereas the probability that he or she will not be wearing one is .30. b. The probability that a randomly selected car is red
A small business performs a service and then bills its customers. From past experience, 90% of the customers pay their bills within a week. a. What is the probability that a randomly selected customer will not pay within a week? b. The business has billed two customers this week. What is the
According to Krantz (1992, p. 111), the probability of being born on a Friday the 13th is about 1/214. a. What is the probability of not being born on a Friday the 13th? b. In any particular year, Friday the 13th can occur once, twice, or three times. Is the probability of being born on Friday the
Suppose the probability that you get an interesting piece of mail on any given weekday is 1y20. Is the probability that you get at least one interesting piece of mail during the week (Monday to Friday) equal to 5/20? Why or why not?
You cross a train track on your drive to work or school. If you get stopped by a train you are late. a. Are the events “stopped by train” and “late for work or school” independent events? Explain. b. Are the events “stopped by train” and “late for work or school” mutually exclusive
On any given day, the probability that a randomly selected adult male in the United States drinks coffee is .51 ( 51%), and the probability that he drinks alcohol is .31 (31%).
Read the definition of “independent events” given in Rule 3. Explain whether each of the following pairs of events is likely to be independent: a. A married couple will vote in an upcoming presidential election. Event A is that the husband votes for the Republican candidate; event B is that the
Read the definition of “independent events” given in Rule 3. Explain whether each of the following pairs of events is likely to be independent: a. Event A is that it snows tomorrow; event B is that the high temperature tomorrow is at least 60 degrees Fahrenheit. b. You buy a lottery ticket,
People are surprised to find that it is not all that uncommon for two people in a group of 20 to 30 people to have the same birthday. We will learn how to find that probability in a later chapter. For now, consider the probability of finding two people who have birthdays in the same month. Make the
A restaurant server knows that the probability that a customer will order coffee is .30, the probability that a customer will order a diet soda is .40, and the probability that a customer will request a glass of water is .70. Explain what is wrong with his reasoning in each of the following. a.
Suppose you routinely check coin-return slots in vending machines to see if they have any money in them. You have found that about 10% of the time you find money. a. What is the probability that you do not find money the next time you check? b. What is the probability that the next time you will
Suppose you play a carnival game that requires you to toss a ball to hit a target. The probability that you will hit the target on each play is .2 and is independent from one try to the next. You win a prize if you hit the target by the third try. a. What is the probability that you hit the target
According to Krantz (1992), the probability of being injured by lightning in any given year is 1/685,000. Assume that the probability remains the same from year to year and that avoiding a strike in one year doesn’t change your probability in the next year. a. What is the probability that someone
Suppose you have to cross a train track on your commute. The probability that you will have to wait for a train is 1/5, or .20. If you don’t have to wait, the com mute takes 15 minutes, but if you have to wait, it takes 20 minutes. a. What is the expected value of the time it takes you to
Suppose the probability that you get an A in any class you take is .3, and the probability that you get a B is .7. To construct a GPA, an A is worth 4.0, and a B is worth 3.0. What is the expected value for your GPA? Would you expect to have this GPA separately for each quarter or semester? Explain.
Remember that the probability that a birth results in a boy is about .51. You offer a bet to an unsuspecting friend. Each day you will call the local hospital and find out how many boys and how many girls were born the previous day. For each girl, you will give your friend $ 1 and for each boy your
In the 3 Spot version of the former California Keno lottery game, the player picked three numbers from 1 to 40. Ten possible winning numbers were then randomly selected. It cost $ 1 to play. The accompanying table shows the possible outcomes. Compute the expected value, the
We have seen many examples for which the term expected value seems to be a misnomer. Construct an example of a situation in which the term expected value would not seem to be a misnomer for what it represents.
According to the U.S. Census Bureau, in 2012, about 68% (.68) of children in the United States were living with both parents, 24.4% (. 244) were living with mother only, 4% (.04) were living with father only, and 3.6% (.036) were not living with either parent. What is the expected value for the
Find out your yearly car insurance cost. If you don’t have a car, find out the yearly cost for a friend or relative. Now assume you will either have an accident or not, and if you do, it will cost the insurance company $ 5000 more than the premium you pay. Calculate what yearly accident
Suppose you wanted to test your extrasensory perception (ESP) ability using an ordinary deck of 52 cards, which has 26 red and 26 black cards. You have a friend shuffle the deck and draw cards at random, replacing the card and reshuffling after each guess. You attempt to guess the color of each
Suppose your are able to obtain a list of the names of everyone in your school and you want to determine the probability that someone randomly selected from your school has the same first name as you. a. Assuming you had the time and energy to do it, how would you go about determining that
In Section 14.2 (page 307), you learned two ways in which relative-frequency probabilities can be determined. Explain which method you think was used to determine the following statement: The probability that a particular flight from New York to San Francisco will be on time is .78.
Which of the two methods for determining relative-frequency probabilities (given in Section 14.2) was used to determine each of the following? a. On any given day, the probability that a randomly selected American adult will read a book for pleasure is .33. b. The probability that a five-card poker
Use your own particular expertise to assign a personal probability to something, such as the probability that a certain sports team will win next week. Now assign a personal probability to another related event. Explain how you determined each probability, and explain how your assignments are
Flip a coin 100 times. Stop each time you have done 10 flips (that is, stop after 10 flips, 20 flips, 30 flips, and so on), and compute the proportion of heads using all of the flips up to that point. Plot that proportion versus the number of flips. Comment on how the plot relates to the
Pick an event that will result in the same outcome for everyone, such as whether it will rain next Saturday. Ask 10 people to assess the probability of that event, and note the variability in their responses. (Don’t let them hear each other’s answers, and make sure you don’t pick something
Find two lottery or casino games that have fixed payoffs and for which the probabilities of each payoff are available. (Some lottery tickets list them on the back of the ticket or on the lottery’s website. Some books about gambling give the payoffs and probabilities for various casino games.) a.
Suppose you wanted to simulate the birthdays (month and day, not year) of the five children in one family. For each child, you tell the computer to choose a number from 1 to 366. This covers all possibilities including February 29. a. Would you tell the computer to make all 366 choices equally
The scenario in this exercise is similar to the one in Exercise 7, except the class size is smaller. Suppose that there are 15 students in your class. Each day the teacher randomly selects one student to show the others how to do the previous night’s homework. Each day, all students are eligible
An airline serves lunch in the first- class cabin. Customers are given a choice of either a sandwich or chicken salad. There are 12 customers in first-class, and the airline loads seven of each meal onboard. You would like to simulate the probability that there will not be enough of one or the
You are competing in a swimming race that has eight contestants starting at the same time, one per lane. Two of your friends are in the race as well. The eight lanes are assigned to the eight swimmers at random, but you hope that you and your two friends will be in three adjacent lanes. You plan to
An intersection has a four-way stop sign but no traffic light. Currently, about 1200 cars use the intersection a day, and the rate of accidents at the intersection is about one every two weeks. The potential benefit of adding a traffic light was studied using a computer simulation by modeling
Suppose that a randomization distribution resulting from the simulation of a chi-square test had 7% of the values at or above the chi- square statistic observed for the real sample. a. What is the estimated p-value for the test? b. What decision would you make for the test, using a level of
Suppose a teacher observed a correlation of 0.38 between age and number of words children could define on a vocabulary test, for a group of nine children aged 7 to 15. The teacher wanted to confirm that there was a correlation between age and vocabulary test scores for the population of children in
Suppose you wanted to simulate the birthdays (month and day, not year) of three children in one family by first choosing a month and then choosing a day. Assume that none of them were born in a leap year. a. What range of numbers would you tell the computer to use to simulate the month? Would you
Three males and three females are given 5 minutes to memorize a list of 25 words, and then asked to recall as many of them as possible. The three males recalled 10, 12, and 14 of the words, for an average of 12 words; the three females recalled 11, 14, and 17 of the words, for an average of 14
Suppose you have two siblings, and all three of you were born in the same month of the year. Explain how you could use simulation to estimate the probability that in a family of three children they are all born in the same month. You do not have to provide exact de-tails about how you would
As a promotion, a cereal brand is offering a prize in each box, and there are four possible prizes. You would like to collect all four prizes, but you only plan to buy six boxes of the cereal before the promotion ends. Assume you have a random number generator that weights all numbers equally in a
Suppose that 55% of the voters in a large city support a particular candidate for mayor and 45% do not support the candidate. A poll of 100 voters will be conducted, and the proportion of them who support the candidate will be found. Assume you have a random number generator that weights all
Suppose that there are 38 students in your class. Each day the teacher randomly selects one student to show the others how to do the previous night’s homework. Each day, all students are eligible and equally likely to be chosen, even if they have been chosen that week already. a. On any given
In Exercise 5, the following scenario was presented: As a promotion, a cereal brand is offering a prize in each box and there are four possible prizes. You would like to collect all four prizes, but you only plan to buy six boxes of the cereal before the promotion ends. For this exercise, you want
In Exercise 6, the following scenario was presented. Suppose that 55% of the voters in a large city support a particular candidate for mayor and 45% do not support the candidate. A poll of 100 voters will be conducted, and the proportion of them who support the candidate will be found. For this
Find a study that was done using simulation to estimate a p-value, probability, or random outcome, similar to the earthquake simulation study described in Case Study 15.1. Or, find a simulation website that allows you to conduct your own simulation study based on expert opinion or existing data.
Find out how to do a permutation test for the difference in means for independent samples, and carry out the test using the data in Exercise 23. State the hypotheses you are testing and the results of the test. Explain how the test was done.
Simulate the situation described in Thought Questions 3, 4, and 5. Assume that the probability of a boy for each birth is 0.51 and the probability of a girl is 0.49. Simulate at least 100 families with four children. Find and report the proportion of your simulated families for which there are no
Explain how an insurance salesperson might try to use each of the following concepts to sell you insurance: a. Anchoring b. Pseudocertainty c. Availability
In the early 1990s, there were approximately 5 billion people in the world. Plous (1993, p. 5) asked readers to estimate how wide a cube-shaped tank would have to be to hold all of the human blood in the world. The correct answer is about 870 feet, but most people give much higher answers. Explain
Explain how the concepts in this chapter account for each of the following scenarios: a. Most people rate death by shark attacks to be much more likely than death by falling airplane parts, yet the chances of dying from the latter are actually 30 times greater (Plous, 1993, p. 121). b. You are a
Give one example of how each of the following concepts has had or might have an unwanted effect on a decision or action in your daily life: a. Conservatism b. Optimism c. Forgotten base rates d. Availability
In this chapter, we learned that one way to lower personal-probability assessments that are too high is to list reasons why you might be wrong. Explain how the availability heuristic might account for this phenomenon.
Which of the concepts in this chapter might contribute to the decision to buy a lottery ticket? Explain.
Suppose you have a friend who is willing to ask her friends a few questions and then, based on their answers, is willing to assess the probability that those friends will get an A in each of their classes. She always assesses the probability to be either .10 or .90. She has made hundreds of these
Refer to the scenarios in Table 16.1 on page 347. Suppose someone stands to gain $ 100,000 in a lawsuit, but there is a 5% chance that something will go wrong and they will get nothing. They are offered a settlement of $ 90,000 if they are willing to drop the lawsuit. a. Using the definition of
Guess at the probability that if you ask five people when their birthdays are, you will find someone born in the same month as you. For simplicity, assume that the probability that a randomly selected person will have the same birth month you have is 1/12. Now use the material from Chapter 14 to
People were asked to give a personal probability assessment of the possible occurrence of each of the following two events (Kahneman, 2011, p. 159): • “A massive flood somewhere in North America next year, in which more than 1000 people drown.” • “An earthquake in California sometime next
“You see a person reading The New York Times on the New York subway. Which of the following is a better bet about the reading stranger?• She has a PhD.• She does not have a college degree” (Kahneman, 2011, p. 151).a. Which of the two statements do you think people would state as more
“ In 2002, a survey of American homeowners who had remodeled their kitchens found that, on average, they had expected the job to cost $ 18,658; in fact, they ended up paying an average of $ 38,769” (Kahneman, 2011, p. 250). The quote is an example of what Kahneman calls the planning fallacy,
Suppose a defense attorney is trying to convince the jury that his client’s wallet, found at the scene of the crime, was actually planted there by his client’s gardener. Here are two possible ways he might present this to the jury: Statement A: The gardener dropped the wallet when no one was
A telephone solicitor recently contacted the author to ask for money for a charity in which typical contributions are in the range of $ 25 to $ 50. The solicitor said, “We are asking for as much as you can give, up to $ 300.00.” Do you think the amount people give would be different if the
Research by Slovic and colleagues (1982) found that people judged that accidents and diseases cause about the same number of deaths in the United States, whereas, in truth, diseases cause about 16 times as many deaths as accidents. Using the material from this chapter, explain why the researchers
Determine which statement (A or B) has a higher probability of being true and explain your answer. Using the material in this chapter, also explain which statement you think a statistically naive person would think had a higher probability. A. A car traveling 120 miles per hour on a two-lane
Design and conduct an experiment to try to elicit misjudgments based on one of the phenomena described in this chapter. Explain exactly what you did and your results.
Find and explain an example of a marketing strategy that uses one of the techniques in this chapter to try to increase the chances that someone will purchase something. Do not use an exact example from the chapter, such as “buy one, get one free.”
Estimate the probability of some event in your life using a personal probability, such as the probability that a person who passes you on the street will be wearing a hat, or the probability that traffic lights will be red when you get to them. Use an event for which you can keep a record of the
Explain why it would be much more surprising if someone were to flip a coin and get six heads in a row after telling you they were going to do so than it would be to simply watch them flip the coin six times and observe six heads in a row.
Comment on the following unusual lottery events, including a probability assessment. a. On September 11, 2002, the first anniversary of the 9/11 attack on the World Trade Center, the winning number for the New York State-lottery was 911. b. To play the Maryland Pick 4 lottery, players choose four
Although it’s not quite true, suppose the probability of having a male child (M) is equal to the probability of having a female child (F). A couple has four children. a. Are they more likely to have FFFF or to have MFFM? Explain your answer. b. Which sequence in part (a) of this exercise would a
Suppose a friend reports that she has just had a string of “bad luck” with her car. She had three major problems in as many months and now has replaced many of the worn parts with new ones. She concludes that it is her turn to be lucky and that she shouldn’t have any more problems for a
A fair coin is flipped six times and the sequence of heads and tails is observed. a. Are the sequences HHHHHH and HTHHTT equally likely? Explain. b. Are the events “A = 6 heads in the 6 tosses” and “B = 3 heads and 3 tails in the 6 tosses” equally likely? Explain. c. Would belief in the law
The University of California at Berkeley Wellness Encyclopedia (1991) contains the following statement in its discussion of HIV testing: “In a high-risk population, virtually all people who test positive will truly be infected, but among people at low risk the false positives will outnumber the
Suppose a rare disease occurs in about 1 out of 1000 people who are like you. A test for the disease has sensitivity of 95% and specificity of 90%. Using the technique described in this chapter, compute the probability that you actually have the disease, given that your test results are positive.
Suppose twin sisters are reunited after not seeing each other since they were 3 years old. They are amazed to find out that they are both married to men named James and that they each have a daughter named Jennifer. Explain why this is not so amazing.
Suppose the sensitivity of a test is .90. Give either the false positive or the false negative rate for the test, and explain which you are providing. Could you provide the other one without additional information? Explain.
In financial situations, are businesses or individuals more likely to make use of expected value for making decisions? Explain.
We learned in this chapter that one idea re-searchers have tested was that when forced to make a decision, people choose the alternative that yields the highest expected value. a. If that were the case, explain which of the following two choices people would make: Choice A: Accept a gift of $ 10.
Refer to the previous exercise, about choosing between a gift and a gamble. Explain how the situation in part (a) resembles the choices people have when they decide whether to buy lottery tickets.
Suppose you are trying to decide whether to park illegally while you attend class. If you get a ticket, the fine is $ 25. If you assess the probability of getting a ticket to be 1/100, what is the expected value for the fine you will have to pay? Under those circumstances, explain whether you would
You are making a hotel reservation and are offered a choice of two rates. The advanced purchase rate is $ 100, but your credit card will be charged immediately and there is no refund, even if you don’t use the room. The flexible rate is $ 140 but you don’t pay anything if you don’t use the
Suppose you are seated next to a stranger on an airplane, and you start discussing various topics such as where you were born (country or state), what your favorite movie of all time is, your spouse’s occupation, and so on. For simplicity, assume that the probability that your details match for
Why is it not surprising that the night before a major airplane crash several people will have dreams about an airplane disaster? If you were one of those people, would you think that some-thing amazing had occurred?
Explain why the story about George D. Bryson, reported in Example 17.1, is not all that surprising.
A statistics professor once made a big blunder by announcing to his class of about 50 students that he was fairly certain that someone in the room would share his birthday. We have already learned that there is a 97% chance that there will be two people in a room of 50 with a common birthday. Given
If you wanted to pretend that you could do psychic readings, you could perform “cold readings” by inviting people you do not know to allow you to tell them about themselves. You would then make a series of statements like “I see that there is some distance between you and your mother that
Find out the sensitivity and specificity of a common medical test. Calculate the probability of a true positive for someone who tests positive with the test, assuming the rate in the population is 1 per 100; then calculate the probability assuming the rate in the population is 1 per 1000.
Ask four friends to tell you their most amazing coincidence story. Use the material in this chapter to assess how surprising each of the stories is to you. Pick one of the stories, and try to approximate the probability of that specific event happening to your friend.
Conduct a survey in which you ask 20 people the two scenarios presented in Thought Question 5 at the beginning of this chapter and discussed in Section 17.5. Record the percentage who choose alternative A over B and the percentage who choose alternative C over D. a. Report your results. Are they
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