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Sensors in parking lots are able to detect and communicate when spaces are filled in a large covered parking garage next to an urban shopping mall. How might the owners of the parking garage use this information both to attract customers and to help the store owners in the mall make business plans?:
2. Satellites send back nearly continuous data on the Earth’s land masses, oceans, and atmosphere from space. How might researchers use this information in both the short and long term to help study changes in the Earth’s climate?
3. An organization awards prizes in six categories to people each year. Their website allows you to look up all the prizes awarded in any year. The data are not listed in a table. Rather you drag a slider to the year and see a list of the awardees for that year. Describe the "who" in this scenario.:
4. Pollsters are interested in predicting the outcome of elections. Give an example of how they might model whether someone is likely to vote.:
5. Meteorologists utilize sophisticated models to predict the weather up to ten days in advance. Give an example of how they might assess their models.:
6. Is it reasonable to conclude that
5.05 % of all U.S. adults think that the higher education system provides an excellent value? Why or why not?:
7. A survey of 299 undergraduate students asked about respondents' diet preference (Carnivore, Omnivore, Vegetarian) and political alignment (Liberal, Moderate, Conservative). A stacked bar chart of the 285 responses is given.
a) Describe what this plot shows using the concept of a conditional distribu-tion.
b) Do you think the differences here are real? Explain.:
8. In an effort to increase the sales of their more expensive larger-sized pizzas, a pizzeria analyzed how its coupons were used by customers in regard to what size pizza they chose. The table below shows the percentage of coupons used for each size of pizza, and the percentage of each type of pizza ordered during a four-month period. Compare the two distributions.:
9. The boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. Some summary statistics are also provided. The extreme outlier is an electric car whose electricity usage is equivalent to 112 miles per gallon. If that electric car is removed from the data set, how will the standard deviation be affected? The IQR?:
10. Does the presence of any outliers affect your overall conclusions about the prices in the four markets?:
11. What summary statistic would be chosen to summarize the center of this distribution? Why?:
12. What summary statistic would be chosen to summarize the spread of this distribution? Why?:
13. The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of combined fuel economy (using an average of driving conditions) in miles per gallon by vehicle type (midsize car, standard pickup truck, or SUV) for 2012 model vehicles. Summarize the fuel economies of the three vehicle types
14. A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the accompanying codes were used. The statistics students analyzing the data were asked to study the relationship between eye and hair color. They provided the accompanying plot. Is their graph appropriate? If so, summarize the findings. If not, explain why not.:
15. The pie chart summarizes the genres of
110 first-run movies released one year
16. The pie chart shows the ratings assigned to 839 first-run movies released in a recent year.:
17. A study of body fat on 250 men collected measurements of 12 body parts as well as the percentage of body fat that the men carried. The first accompanying display is a dotplot of their bicep circumferences (in centimeters). The second accompanying display was formed by dividing each measurement by 2.54 to convert it to inches. Do the two dot plots look different? What might account for that?:
18. A university teacher saved every e-mail from students in a large introductory statistics class during an entire term. He then counted, for each student who had sent him at least one e-mail, how many e-mails each student had sent. What does the accompanying histogram say about the distribution of e-mails sent by students?:
19. The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.:
20. The accompanying histogram shows the total number of adoptions in each of 43 regions. Determine whether the mean number of adoptions or the median number of adoptions is higher. Why?:
21. The pie chart given to the right and bar chart given below summarize the movie genres of all the films shown in a suburban theatre over the course of one year. Complete parts a and b.:
22. The Centers for Disease Control lists causes of death in the United States during 2013. (Each person is assigned only one cause of death.):
23. A clerk entering salary data into a company spreadsheet accidentally put an extra "0 " in the boss's salary, listing it as $2,400,000 instead of $240,000. Explain how this error will affect these summary statistics for the company payroll.
a) measures of center (median and mean)
b) measures of spread (range, IQR, and standard deviation):
24. People with z-scores of 2.25 or above on a certain aptitude test are sometimes classified as geniuses. If aptitude test scores have a mean of 100 and a standard deviation of 16 points, what is the minimum aptitude test score needed to be considered a genius?: 136
25. A town's January high temperatures average 37°F with a standard deviation of 10° , while in July the mean high temperature is 72° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 53° ? Explain.:
26. A company selling clothing on the Internet reports that the packages it ships have a median weight of 59 ounces and an IQR of 24 ounces.
a) The company plans to include a sales flyer weighing 5 ounces in each package. What will the new median and IQR be?
b) If the company recorded the shipping weights of the packages with the sales flyers included in pounds instead of ounces, what would the median and IQR be?:
27. Fuel economy estimates for automobiles built one year predicted a mean of 27.2 mpg and a standard deviation of 5.8 mpg for highway driving. Assume that a Normal model can be applied. Use the 68 95 99.7 Rule to complete parts a) through e).:
28. A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 19.:
29. Corey has 4929 songs in his computer's music library. The songs have a mean duration of 244.7 seconds with a standard deviation of 110.31 seconds.
One of the songs is 382 seconds long. What is its z-score?: 1.24
30. A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(750 ,50 ). Use the 68-95-99.7 Rule to complete parts a) through c) below.:
31. Use the Normal model N(1134 ,79 ) for the weights of steers.
a) What weight represents the 66th percentile?
b) What weight represents the 93rd percentile?
c) What's the IQR of the weights of these steers?:
32. Correlation Properties: - if close to -1 or 1: strong
33. A larger firm is considering acquiring a small bookstore. An analyst for the firm, noting that there is a strong, positive relationship between the number of sales people working and the amount of sales, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion justified? What alternative explanations can you offer? Use appropriate statistics terminology.:
34. A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more plows whenever it snows because, he says, that will increase business. Comment on the director's conclusion.:
35. Suppose data was collected for each pair of variables below to make a scatterplot. Which variable would be used as the explanatory variable and which as the response variable? Why? What is expected in the scatterplot? Discuss the likely direction, form, and strength for parts a through d below.:
36. In a study of streams in the Adirondack Mountains, the following relationship was found between the water's pH and its hardness (measured in grains). Is it appropriate to summarize the strength of association with a correlation?:
37. A study of traffic delays in 68 cities found the relationship shown in the scatterplot to the right between Total Delay (in total hours lost) and Mean Highway Speed.
Is it appropriate to summarize the strength of association with a correlation? Explain.:
Is there an association between time of year and the nighttime temperature in North Dakota? A researcher assigned the numbers 1-365 to the days January 1-December 31 and recorded the temperature at 2:00 a.m. for each. What might you expect the correlation between DayNumber and Temperature to be? Explain.: 0.
38. A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0. Discouraged, he didn't bother making a scatterplot. Explain to him how the scatterplot could still reveal the strong association he anticipated.:
39. The errors in predicting hurricane tracks are given in nautical miles. A statutory mile is 0.86898 nautical mile. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in statutory miles rather than nautical miles. Explain why converting the errors to miles would not change the correlation between Prediction Error and Year.:
40. A survey of the world's nations in 2014 shows a strong positive correlation between percentage of the country using smart phones and life expectancy in years at birth.:
41. Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present (none= 1, little= 2, some= 3, much= 4, extreme= 5) and presence of Heart Disease (No= 0, Yes= 1). They found a correlation of 0.089 between the two variables. Comment on their conclusion that this shows that baldness is not a possible cause of heart disease.:
42. Even though it is represented by numbers, this is categorical data and not suitable for correlation.:
43. Least squares means that some of the squares of the residuals are minimized:
44. We write y^ to denote the predicted values and y to denote the observed values.:
45. A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is
weight= 5.95+0.1769 length. Explain in words what this model means. Should new parents (who tend to worry) be concerned if their newborn's length and weight don't fit this equation?:
residual:
46. For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in serving of 77 breakfast cereals produced the regression model Potassium=38+27Fiber. From this model you can estimate a cereal's potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual?: The potassium content is actually lower than the model predicts for a cereal with that much fiber.
47. A regression model uses a car's engine displacement to estimate its fuel economy. In this context, what does it mean to say that a certain car has a positive residual?:
48. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings of 77 breakfast cereals produced the regression model Potassium=35+27Fiber. Explain what the slope means.:
49. Analysis of the relationship between the fuel economy (mpg) and engine size (in liters) for 35 models of cars produces the regression model mpg=36.55 3.843•Engine size. Explain what the slope means.:
50. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings of 77 breakfast cereals produced the regression model Potassium=39+29Fiber and se=30.84.
Explain in this context what se=30.84 means.:
51. A regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and size is in square feet.
Price=47.82+0.068 (Size)
a) Explain what the slope of the line says about housing prices and house size.
b) What price would you predict for a 3000 -square-foot house in this market?
c) A real estate agent shows a potential buyer a 1100 -square-foot house, saying that the asking price is $6000 less than what one would expect to pay for a house of this size. What is the asking price, and what is the $6000 called?:
54. Administrators at a university were interested in estimating the percentage of students who plan on going abroad during college. The university's student body has about 44,000 members. How might the administrators answer their question by applying the three Big Ideas?:
55. The managers of a large company wished to know the percentage of employees who feel "extremely satisfied" to work there. The company has roughly 28,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 491 completed responses. How does their study deal with the three Big Ideas of sampling?:
56. The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of current students who are the first in their families to attend college. Explain to the president the difference between the proportion of respondents who are first attenders and the proportion of the entire student body that are first attenders. Use appropriate statistics terminology.:
57. The company's annual report states, "Our survey shows that 84.28 % of our employees are 'very happy' working here." Comment on that claim. Use appropriate statistics terminology.:
58. A professor teaching a large lecture class of 450 students wants to sample her class. To do this, she rolls a die to determine the first row to hand out a survey to. Then, she also hands out the survey to every sixth row after this first row. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific.:
59. Administrators at a university were interested in estimating the percentage of students who are the first in their family to go to college. The university student body has about 48,000 members.:
60. The managers of a large company wished to know the percentage of employees who feel "extremely satisfied" to work there. The company has roughly 40,000 employees. Three scenarios are given in parts a through c below. For each scenario, determine the sampling method used by the managers.:
61. What problems do you see with asking the following question of students? "Are you the first member of your family to seek higher education?":
62. The company plans to have the manager of each corporate division hold a meeting of their employees to ask whether they are unhappy on their jobs. They will ask people to raise their hands to indicate whether they are unhappy. What problems do you see with this plan?:
63. Administrators at a university were interested in estimating the percentage of students who are the first in their family to go to college. The university student body has about 49,000 members. The university administration is considering a variety of ways to sample students for a survey. For each of these proposed survey designs, identify the problem.:
64. An internet company conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 13-65. Their samples are designed so that they get 500 males and 500 females in each country.:
65. An ice hockey organization tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 20 players on the team. Each testing day can be considered a study of drug use.:
66. definition chap 10
67. At its website, a polling company publishes results of a new survey each day. Scroll down to the end of the published results and you'll find a statement that includes words as shown below.
Results are based on telephone interviews with 1,008 national adults, aged 18 and older, conducted on April 2-5, 2007 ... In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.:
68. For the following report about a statistical study, identify (if possible) a) the population; b) the population parameter of interest; c) the sampling frame; d) the sample; e) the sampling method, including whether or not randomization was employed; f) who (if anyone) was left out of the study; and g) any potential sources of bias you can detect and any problems you see in generalizing to the population of interest.
A US consumer magazine asked all adult subscribers whether they had used experimental medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 17 % of those responding reported cures or substantial improvement in their condition.:
69. An environmental agency took soil samples at 14 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.:
70. A company packaging potato chips maintains quality control by randomly selecting 20 cases from each day's production and weighing the bags. Then they open four random bags from each case and inspect the contents.:
71. A local TV station conducted a "Pulse-Poll" about the upcoming mayoral election. Evening news viewers were invited to text in their votes, with the results being announced on the late-night news. Based on the texts, the station predicted that the current mayor would win the election with 52% of the vote. They were wrong and the mayor lost, getting only 46% of the vote. Do you think the station's faulty prediction is more likely to be a result of bias or sampling error? Explain.:
72. Prior to a mayoral election, a newspaper conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Candidate A would win the election with 52% of the vote. The newspaper was wrong: Candidate A lost, getting only 46% of the vote. Do you think the newspaper's faulty prediction is more likely to be a result of bias or sampling error? Explain.:
73. In a large city school system with 49 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. Assume the schools are homogeneous and differ from each other.:
74. For your political science class, you'd like to take a survey from a sample of all the Orthodox Church members in your region. A list of places of worship shows 21 Orthodox churches in the area. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches , you will ask to get a list of all current members and contact 100 members at random:
Some people have been complaining that the children's playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt. They hand out questionnaires to parents who bring children to the park. Describe some possible biases in this sample.:
75. A recent public survey asked the following question.
"Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park?":
76. Two members of the PTA committee have proposed the accompanying questions to ask in seeking parent's opinions. Question 1 is "Should elementary school-age children have to pass high-stakes tests in order to remain with their classmates?" and Question 2 is "Should schools and students be held accountable for meeting yearly learning goals by testing students before they advance to the next grade?" Complete parts a and b below.:
77. Should companies that promote teen smoking be liable to help pay for the costs of cancer institutions ?:
78. Given that 16-year-olds are old enough to drive , is it fair to set the gambling age at:
80. Anytime a survey is conducted, care must be taken to avoid undercoverage. Suppose a firm selects 500 names from a city phone book, calls their homes between noon and 4 p.m., and interviews whoever answers, anticipating contacts with at least 200 people.:
81. Consider drawing a random sample only from landline phone exchanges. Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non-landline (cell phone) exchanges. Do you think these advantages and disadvantages have changed over time? How do you expect they'll change in the future?:
82. Occasionally, when Josh fills his car with gas, he figures out how many miles per gallon his car got. He wrote down those results after five fill-ups in the past few months. Overall, it appears that his car gets 21.5 miles per gallon.:
83. Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed properly. Complete parts a and b below.
84. Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At the end of the week, the scientists said that 22 % of the 338 fish that were submitted for inspection displayed the discoloration. From this information, can the researchers estimate what proportion of fish in the river have discolored scales? Explain.:
85. Which matters more about a sample you draw from a population?:
86. You are trying to study the amount of financial aid students at your University receive. You sample 50 students and find out the average size of their financial aid packages. The average of your sample is a:
87. You are doing a study for a non-profit group helping at-risk children in your city. Suppose you know that 14.2% of the children in your city live in poverty.
This percentage is an example of a:
88. You recently began an internship at your local chapter of savethepigeons.com. Concerned about a city ballot initiative dealing with the environment, you conduct a telephone survey of local residents. What are some possible sources of bias in your results?:
89. If you create an online survey, individuals can choose on their own whether to participate in the sample. This causes a form of bias called:
90. When you sample so that every combination of individuals in your population has an equal chance of being chosen you are taking a:
91. A friend of yours in your intro stats class obtains permission to randomly sample the University student body to conduct a satisfaction survey on some recent changes to the enrollment process. She randomly samples 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. This is an example of a:
92. Some friends of yours in a political science class are angry about a new town ordinance restricting off-campus parties. They make an online survey asking students' opinions. This type of sampling might be classified as
93. Flipping a fair coin is said to randomly generate heads and tails with equal probability. Explain what random means in this context.:
94. A friend says "I flipped five heads in a row! The next one has to be tails!" Explain why this thinking is incorrect.:
95. A national survey found that 50 % of adults ages 25-29 had only a cell phone and no landline. Suppose that five 25-29-year-olds are randomly selected. Complete parts a through c below.:
96. Suppose that 19 % of people have a dog , 29 % of people have a cat , and 7 % of people own both. What is the probability that someone owns a dog or a cat ?:
97. What is the probability that a person likes to watch football, given that she also likes to watch basketball?
Basketball 27 8
No_Basketball 39 26:
98. A student figures that he has a 32 % chance of being let out of class late. If he leaves class late, there is a 60 % chance that he will miss his train. What is the probability that he gets out of class late and misses the train?:
99. A nervous kicker usually makes 82 % of his first field goal attempts. If he makes his first attempt, his success rate rises to 89 %. What is the probability that he makes his first two kicks?:
100. On a certain ship that sank, the probability of survival was 0.394. Among first class passengers, it was 0.794. Were survival and ticket class independent? Explain.:
101. If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.:
102. For each of the following, list the sample space and tell whether you think the events are equally likely:
a) Roll two dice; record the sum of the numbers
b) A family has 3 children; record each child's sex in order of birth
c) Toss four coins; record the number of tails
d) Toss a coin 10 times; record the length of the longest run of heads:
103. A casino claims that its roulette wheel is truly random. What should that claim mean?:
104. The weather reporter on TV makes predictions such as a 25% chance of rain. What is the meaning of such a phrase?:
105. After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." Explain what he's trying to say, and comment on the validity of his reasoning.:
106. Recently, a casino issued a press release announcing that a cocktail waitress won the world's largest slot jackpot—over $30,000,000. She said she had played less than $50 in the machine when the jackpot hit. The top jackpot for this type of slot machine builds from a base amount of $7 million and can be won with a 3-coin ($3) bet.:
107. Suppose that 36 % of families living in a certain country own a desktop computer and 21 % own a laptop. The Addition Rule might suggest, then, that 57 % of families own either a desktop computer or a laptop. What's wrong with that reasoning?:
108. Funding for many schools comes from taxes based on assessed values of local properties. People's homes are assessed higher if they have extra features such as garages and hot tubs. Assessment records in a certain school district indicate that 30 % of the homes have garages and
5 % have hot tubs. The Addition Rule might suggest, then, that 35 % of residences have a garage or a hot tub. What is wrong with that reasoning?:
109. Traffic checks on a certain section of highway suggest that 70% of drivers are speeding there. Since 0.7×0.7=0.49 , the multiplication rule might suggest that there is a 49% chance that two vehicles in a row are both speeding. What's wrong with that reasoning?:
110. A consumer organization estimates that over a 1-year period 17 % of cars will need to be repaired once, 5 % will need repairs twice, and 1 % will require three or more repairs:
111. In a large introductory statistics lecture hall, the professor reports that 60 % of the students enrolled have never taken a calculus course, 30 % have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two groupmates:
112. You were randomly assigned to be part of a group of three students from an Intro Stats class in which 55% of the students had never taken a Calculus course, 32% of students had taken only one semester of Calculus, and the rest had taken two or more semesters of Calculus. The Multiplication Rule was used to calculate the probability that neither of your other two groupmates had studied Calculus.:
113. A certain bowler can bowl a strike 70% of the time. What is the probability that she
a) goes three consecutive frames without a strike?
b) makes her first strike in the third frame?
c) has at least one strike in the first three frames?
d) bowls a perfect game (12 consecutive strikes)?:
114. You purchased a five-pack of new light bulbs that were recalled because 11 % of the lights did not work. What is the probability that at least one of your lights is defective?:
115. For a sales promotion, the manufacturer places winning symbols under the caps of 21% of all its soda bottles. If you buy a six-pack of soda, what is the probability that you win something?:
116. The prerequisite for a required course is that students must have taken either course A or course B. By the time they are juniors, 52 % of the students have taken course A, 23% have had course B, and 12 % have done both. a) What percent of the juniors are ineligible for the course?
b) What's the probability that a junior who has taken course A has also taken course B?
c) Are taking these two courses disjoint events? Explain.
d) Are taking these two courses independent events? Explain.: a)
117. Your neighbor has bought a lottery ticket once a week for the last 10 years. He has not yet won, but feels his time is due. His chance of winning on the next ticket he buys is __________ the first one he ever bought.:
118. The property which states that for independent trials, as the number of trials increases, the long run relative frequency of an outcome gets closer to the true probability is called the __________.: law of large numbers
119. A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.:
120. In one city, 47.5% of adults are female, 10.2% of adults are left-handed, and 4.8% are females who are left handed. For an adult selected at random from the city, let
F=event
the person is female L=event the person is left-handed.
Find P(F or L). Round to three decimal places
121. In a Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth.
What is the probability that a student from this class eats breakfast but does NOT floss?:
122. An investment website can tell what devices are used to access their site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way. They draw a random sample of 451 investors from their customers. Suppose that the true proportion of smartphone users is 31 %:
123. The proportion of adult women in a certain geographical region is approximately 48 %. A marketing survey telephones 500 people at random.:
124. A research company polled a random sample of 930 teens about Internet use. 56 % of those teens reported going online several times a day—a fact of great interest to advertisers. Complete parts a through c below.:
125. According to a research survey,
28 % of adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1600 people from a much larger body of adults. Is it reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion? Why or why not?:
126. For her final project, Stacy plans on surveying a random sample of 40 students on whether they plan to go to Florida for Spring Break. From past years, she guesses that about 12 % of the class goes. Is it reasonable for her to use a Normal model for the sampling distribution of the sample proportion? Why or why not?:
127. The distribution of scores on a test for a particular class is skewed to the left. The professor wants to predict the maximum score and understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 34 different tests (with n = 5). The histogram to the right shows a simulated sampling distribution of the sample maximum from these tests. Complete parts a) and b) below.:
128. A research company polled a random sample of 799 U.S. teens about Internet use. 49% of those teens reported going online several times a day—a fact of great interest to advertisers. The 95% confidence interval for this number is from 45.6% to 52.5%. Complete parts a and b below.:
129. In a research study on trends in marriage and family, 5 %
of randomly selected parents said that they never spank their children. The
95% confidence interval is from
3.8 % to 6.2 % (n=1207 :).
130. A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 2390 adults whether they think things in the country are going in the right direction or in the wrong direction.
70 % said that things were going in the wrong direction. Complete parts a and b below.:
131. Finding Appropriate z*-Values for Given Confidence Levels:
132. A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 386 adults whether they think things in the country are going in the right direction or in the wrong direction. 58 % said that things were going in the wrong direction. Complete parts a and b below.:
133. It's believed that as many as
21 % of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.:
134. In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.:
135. A TV newscaster reports the results of a poll of voters, and then says, "The margin of error is plus or minus
5 %." Explain carefully what that means.:
136. A medical researcher estimates the percentage of children exposed to lead-based paint, adding that he believes his estimate has a margin of error of about 10 %. Explain what the margin of error means.:
137. For each situation described below, identify the population and the sample, explain what p and p^ represent, and tell whether it is appropriate to create a one-proportion z-interval
138. For a given sample size, higher confidence means a smaller margin of error.:
139. For a specified confidence level, larger samples provide smaller margins of error.:
140. For a fixed margin of error, larger samples provide greater confidence.: true
141. For a given confidence level, halving the margin of error requires a sample size twice as large
142. A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wants to estimate the fraction of cars in the United States that are made in Japan. The computer output to the right summarizes the results of a random sample of 50 autos. Explain carefully what it tells you.:
143. A study of 939 decision (to grant parole or not) made by a parole board produced the provided computer output. Assuming these cases are representative of all cases that may come before the board, what can be concluded?:
144. Of 535 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared to standard gene fragments that can identify the species, 29 % were mislabeled.:
145. A poll taken this year asked 1019 adults whether they were fans of a particular sport and 38 % said they were. Last year, 43% of a similar-size sample had reported being fans of the sport. Complete parts a through e below.
146. A philanthropic organisation sent free mailing labels and greeting cards to a random sample of
100,000 potential donors on their mailing list and received 5105 donations.:
147. An insurance company checks police records on 584 accidents selected at random and notes that teenagers were at the wheel in 81 of them.
148. Some food retailers propose subjecting food to a low level of radiation in order to improve safety, but sale of such “irradiated" food is opposed by many people. Suppose a grocer wants to find out what his customers think. He has cashiers distribute surveys at checkout and ask customers to fill them out and drop them in a box near the front door. He gets responses from 110 customers, of whom 71 oppose the radiation treatments. What can the grocer conclude about the opinions of all his customers?
149. It's believed that as many as
24 % of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 3 %?:
150. Editors preparing a report on the economy are trying to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. They are willing to accept a margin of error of 4 % but want 95 % confidence. How many randomly selected employers will they need to contact?: n=(1.960)^2(0.25)/(0?04)^2
n=600
151. Assume that 10% of students at a university wear contact lenses. We randomly pick 200 students. What is the standard deviation of the proportion of students in this group who may wear contact lenses? Round to two decimal places.: 2.12%
152. Assume that 15% of students at a university wear contact lenses. We randomly pick 200 students. What is the mean of the proportion of students in this group who may wear contact lenses?:
153. A university’s administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation. In previous years, the percentage averaged 15%. He wants the margin of error to be within 5% at a 99% confidence level. What sample size will suffice? Round to the nearest integer.:
154. A food company sells salmon to various customers. The mean weight of the salmon is 27 lb with a standard deviation of 2 lbs. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 49 salmon, and to discount outlet stores in pallets of 81 salmon. To forecast costs, the shipping department needs to estimate the standard deviation of the mean weight of the salmon in each type of shipment.
155. A waitress believes the distribution of her tips has a model that is slightly skewed to the right , with a mean of $9.60 and a standard deviation of $5.40. She
usually waits on about 40
parties over a weekend of work.:
156. Describe how the shape, center, and spread of t -models change as the number of degrees of freedom increases.:
157. survey finds that a 95% confidence interval for the mean salary of a police patrol officer in a certain city in a recent year is $52,516 to $53,509. A student is surprised that so few police officers make more than $53,509. Explain what is wrong with the student's interpretation.:
158. A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student's t-based confidence interval: With 95.00 % Confidence, 66.372986<¼ (Pulse)<:
159. What are the chances your flight will leave on time? To the right are a histogram and summary statistics for the percentage of flights departing on time each month from 2001 thru 2006.:
160. Will your flight get you to your destination on time? To the right are a histogram and summary statistics for the percentage of delayed arrivals each month from 2001 thru 2006. Consider these data to be a representative sample of all months. There is no evidence of a time trend. (The correlation of Flights Delayed % with time is r= 0.004 .):
161. A study measured the waist size of 975 men , finding a mean of 36.36 inches and a standard deviation of 3.95 inches. A histogram of these measurements is shown to the right.:
162. A college's data about the incoming freshmen indicates that the mean of their high school GPAs was 3.3 , with a standard deviation of 0.35 ; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of
25.: Describe the appropriate sampling distribution model, including shape, center, and spread. N(3.3,0.07). What assumptions and conditions must be satisfied for the sampling distribution model to be appropriate? Select all that apply.
163. Suppose we want to estimate the proportion of defective items produced by a manufacturing process. Could we use the methods of this chapter to answer this question? no
164. On a final project in an introductory statistics class, a student reports a 95% confidence interval for the average cost of a haircut to be ($5.50,$65.00). What is the correct interpretation of this confidence interval?:
165. A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $28 and a standard deviation of $15. Suppose the store had 296 customers this Sunday.:
A survey of senior citizens at a doctor's office shows that 40% take blood pressure-lowering medication, 47% take cholesterol-lowering medication, and 13% take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?:
166. A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If 55% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied some statistics?:
167. A professor divided the students in her business class into three groups:
those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If 10% of the students have never taken a statistics class, 35% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that both of the first two groupmates you meet have studied at least one semester of statistics?:
168. A professor divided the students in her business class into three groups:
those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If 35% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that neither of the first two groupmates you meet has studied any statistics?:
169. Political analysts estimate the probability that Candidate A will run for president in 2016 is 45%, and the probability that Candidate B will run is 20%.
If their political decisions are independent, then what is the probability that only Candidate A runs for president?:
170. Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the mean of the proportion of clients in this group who may not make timely payments?:
171. In a survey of 300 T.V. viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs. Round to two decimal places.:
172.
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