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business statistics in practice
The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions
Describe how the sample size and confidence level affect the length of a confidence interval.
Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval.
What’s the probability that our 95% confidence interval captures the parameter?
Got shoes? How many pairs of shoes, on average, do female teens have? To find out, an AP® Statistics class conducted a survey. They selected an SRS of 20 female students from their school. Then they recorded the number of pairs of shoes that each student reported having. Here are the data:50 26 26
Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population variance s2.
Going to the prom Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.
Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19 answered “Yes.”3
NA EP scores Young people have a better chance of full-time employment and good wages if they are good with numbers. How strong are the quantitative skills of young Americans of working age?One source of data is the National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment
Auto emissions Oxides of nitrogen (called NOX for short) emitted by cars and trucks are important contributors to air pollution. The amount of NOX emitted by a particular model varies from vehicle to vehicle. For one light-truck model, NOX emissions vary with mean m = 1.8 grams per mile and
NA EP scores Refer to Exercise 5. Below your sketch, choose one value of x– inside the shaded region and draw its corresponding confidence interval.Do the same for one value of x– outside the shaded region. What is the most important difference between these intervals? (Use Figure 8.5, on page
Prayer in school A New York Times/CBS News Poll asked a random sample of U.S. adults the question,“Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Based on this poll, the 95% confidence interval for the population proportion who favor such an
Losing weight A Gallup Poll asked a random sample of U.S. adults, “Would you like to lose weight?”Based on this poll, the 95% confidence interval for the population proportion who want to lose weight is(0.56, 0.62).5(a) Interpret the confidence interval.(b) What is the point estimate that was
Prayer in school Refer to Exercise 9. The news article goes on to say: “The theoretical errors do not take into account cadditional error resulting from the various practical difficulties in taking any survey of public opinion.” List some of the “practical difficulties”that may cause errors
Losing weight Refer to Exercise 10. As Gallup indicates, the 3 percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “nonsampling errors”) could affect the accuracy of
Shoes The AP® Statistics class in Exercise 1 also asked an SRS of 20 boys at their school how many pairs of shoes they have. A 95% confidence interval for the difference in the population means (girls – boys) is 10.9 to 26.5. Interpret the confidence interval and the confidence level.
Lying online Many teens have posted profiles on sites such as Facebook. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170 younger teens (ages 12 to 14) polled, 117 said “Yes.”Of 317 older teens (ages 15 to 17) polled,
Shoes Refer to Exercise 15. Does the confidence interval give convincing evidence of a difference in the population mean number of pairs of shoes for boys and girls at the school? Justify your answer.
Lying online Refer to Exercise 16. Does the confidence interval give convincing evidence of a difference in the population proportions of younger and older teens who include false information in their profiles? Justify your answer.
Explaining confidence A 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. Discuss whether each of the following explanations is correct.(a) We are confident that 95% of all young women have BMI between 26.2 and 27.4.(b) We are 95% confident that
Explaining confidence The admissions director from Big City University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct.(a) There is a 95% probability that the interval from 107.8 to 116.2
The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95%confidence interval, a 99% confidence interval will be(a) narrower and would involve a larger risk of being incorrect.(b) wider and would involve a smaller risk of being incorrect.(c) narrower and
The researcher is deciding between a sample of size n = 500 and a sample of size n = 1000. Compared to using a sample size of n = 500, a 95% confidence interval based on a sample size of n = 1000 will be(a) narrower and would involve a larger risk of being incorrect.(b) wider and would involve a
In a poll, I. Some people refused to answer questions.II. People without telephones could not be in the sample.III. Some people never answered the phone in several calls.Which of these possible sources of bias is included in the ±2% margin of error announced for the poll?(a) I only (c) III only
You have measured the systolic blood pressure of an SRS of 25 company employees. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements is true?(a) 95% of the sample of employees have a systolic blood
Power lines and cancer (4.2, 4.3) Does living near power lines cause leukemia in children? The National Cancer Institute spent 5 years and $5 million gathering data on this question. The researchers compared 638 children who had leukemia with 620 who did not. They went into the homes and measured
Sisters and brothers (3.1, 3.2) How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs:8 Brother: 71 68 66 67 70 71 70 73 72 65 66 Sister: 69 64 65 63 65 62 65 64 66 59 62 (a) Construct a scatterplot using brother’s
State and check the Random, 10%, and Large Counts conditions for constructing a confidence interval for a population proportion.
Determine critical values for calculating a C % confidence interval for a population proportion using a table or technology.
Construct and interpret a confidence interval for a population proportion.
Determine the sample size required to obtain a C %confidence interval for a population proportion with a specified margin of error.
Rating school food Latoya wants to estimate what proportion of the seniors at her boarding high school like the cafeteria food. She interviews an SRS of 50 of the 175 seniors living in the dormitory. She finds that 14 think the cafeteria food is good.
High tuition costs Glenn wonders what proportion of the students at his school believe that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.
AIDS and risk factors In the National AIDS Behavioral Surveys sample of 2673 adult heterosexuals, 0.2% had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS.We want to estimate the proportion p in the population who share these two risk factors.
Whelks and mussels The small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells.Whelks often drill into mussels, but this behavior appears to be more or less common in different locations. Researchers collected whelk eggs from the
98% confidence Find z* for a 98% confidence interval using Table A or your calculator. Show your method.
93% confidence Find z* for a 93% confidence interval using Table A or your calculator. Show your method.
Going to the prom Tonya wants to estimate what proportion of her school’s seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.(a) Identify the population and parameter of interest.(b) Check conditions for
Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19 answered “Yes.”12(a)
Binge drinking In a recent National Survey of Drug Use and Health, 2312 of 5914 randomly selected full-time U.S. college students were classified as binge drinkers.13(a) Calculate and interpret a 99% confidence interval for the population proportion p that are binge drinkers.(b) A newspaper article
Teens’ texting A Pew Internet and American Life Project survey found that 392 of 799 randomly selected teens reported texting with their friends every day.(a) Calculate and interpret a 95% confidence interval for the population proportion p that would report texting with their friends every
Binge drinking Describe a possible source of error that is not included in the margin of error for the 99% confidence interval in Exercise 35.
Teens’ texting Describe a possible source of error that is not included in the margin of error for the 95% confidence interval in Exercise 36.
How common is SAT coaching? A random sample of students who took the SAT college entrance examination twice found that 427 of the respondents had paid for coaching courses and that the remaining 2733 had not.14 Construct and interpret a 99%confidence interval for the proportion of coaching among
2010 begins In January 2010 a Gallup Poll asked a random sample of adults, “In general, are you satisfied or dissatisfied with the way things are going in the United States at this time?” In all, 256 said that they were satisfied and the remaining 769 said they were not. Construct and interpret
Equality for women? Have efforts to promote equality for women gone far enough in the United States?A poll on this issue by the cable network MSNBC contacted 1019 adults. A newspaper article about the poll said, “Results have a margin of sampling error of plus or minus 3 percentage
A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the 2372 calls, 1921 oppose the ban.The station, following recommended practice, makes a confidence statement: “81% of the Channel 13 Pulse Poll sample opposed the ban. We can be
Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and
School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.(a) How large an SRS is required to obtain a margin of error
Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need?
Starting a nightclub A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment.What sample size is required to
Teens and their TV sets According to a Gallup Poll report, 64% of teens aged 13 to 17 have TVs in their rooms. Here is part of the footnote to this report:These results are based on telephone interviews with a randomly selected national sample of 1028 teenagers in the Gallup Poll Panel of
Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics.Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gamblingrelated behaviors.17 Of the 5594 Division I male
A Gallup Poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95% confidence level.This means that (a) the poll used a method that gets an answer within 3%of the truth about the
Most people can roll their tongues, but many can’t.The ability to roll the tongue is genetically determined.Suppose we are interested in determining what proportion of students can roll their tongues.We test a simple random sample of 400 students and find that 317 can roll their tongues. The
You want to design a study to estimate the proportion of students at your school who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval, and you would like the margin
A newspaper reporter asked an SRS of 100 residents in a large city for their opinion about the mayor’s job performance. Using the results from the sample, the C% confidence interval for the proportion of all residents in the city who approve of the mayor’s job performance is 0.565 to 0.695.
Accidents happen (1.2, 3.1)(a) Construct a plot that displays the distribution of the number of accidents effectively.(b) Construct a plot that shows the relationship between the number of accidents and the time when they occurred.(c) Describe something that the plot in part (a) tells you about the
Accidents happen (1.3) Plant managers are concerned that the number of accidents may be significantly higher during the midnight to 8:00 a.m.shift than during the 4:00 p.m. to midnight shift.What would you tell them? Give appropriate statistical evidence to support your conclusion.
State and check the Random, 10%, and Normal/Large Sample conditions for constructing a confidence interval for a population mean.
Explain how the t distributions are different from the standard Normal distribution and why it is necessary to use a t distribution when calculating a confidence interval for a population mean.
Determine critical values for calculating a C% confidence interval for a population mean using a table or technology.
Construct and interpret a confidence interval for a population mean.
Determine the sample size required to obtain a C%confidence interval for a population mean with a specified margin of error.
Critical values What critical value t* from Table B would you use for a confidence interval for the population mean in each of the following situations?(a) A 95% confidence interval based on n = 10 randomly selected observations(b) A 99% confidence interval from an SRS of 20 observations(c) A 90%
Critical values What critical value t* from Table B should be used for a confidence interval for the population mean in each of the following situations?(a) A 90% confidence interval based on n = 12 randomly selected observations(b) A 95% confidence interval from an SRS of 30 observations(c) A 99%
Blood pressure A medical study finds that x– = 114.9 and sx = 9.3 for the seated systolic blood pressure of the 27 members of one treatment group. What is the standard error of the mean? Interpret this value in context.
Travel time to work A study of commuting times reports the travel times to work of a random sample of 20 employed adults in New York State. The mean is x– = 31.25 minutes, and the standard deviation is sx = 21.88 minutes. What is the standard error of the mean? Interpret this value in context.
Willows in Yellowstone Writers in some fields summarize data by giving x– and its standard error rather than x– and sx. Biologists studying willow plants in Yellowstone National Park reported their results in a table with columns labeled x– ± SE. The table entry for the heights of willow
Blink When two lights close together blink alternately, we “see” one light moving back and forth if the time between blinks is short. What is the longest interval of time between blinks that preserves the illusion of motion?Ask subjects to turn a knob that slows the blinking until they
Bone loss by nursing mothers Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47 randomly selected mothers during three
Reading scores in Atlanta The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts.TUDA gives a reading test scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.” Scores
Men and muscle Ask young men to estimate their own degree of body muscle by choosing from a set of 100 photos. Then ask them to choose what they believe women prefer. The researchers know the actual degree of muscle, measured as kilograms per square meter of fat-free mass, for each of the photos.
A big-toe problem A bunion on the big toe is fairly uncommon in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity on the big toe in a random sample of 37 patients under the age of 21 who came to a medical center for surgery to correct a bunion. The
Give it some gas! Computers in some vehicles calculate various quantities related to performance.One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled
Vitamin C content Several years ago, the U.S.Agency for International Development provided 238,300 metric tons of corn-soy blend (CSB) for emergency relief in countries throughout the world.CSB is a highly nutritious, low-cost fortified food.As part of a study to evaluate appropriate vitamin C
Paired tires Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained.Both methods were used to estimate
Water Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of 10 randomly selected wells in a large region.The data are provided in the table
Estimating BMI The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI m in this population to within ±1 with 99% confidence? Show your work.
The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points. How large a sample of high school students would be needed to estimate the mean change
One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that(a) z can be used only for large samples.(b) z requires that you know the population standard deviation s.(c) z requires
You have an SRS of 23 observations from a large population.The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?(a) 2.177 (b) 2.183 (c) 2.326 (d) 2.500 (e) 2.508
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content m?(a) 90% confidence; n = 25(b) 90% confidence; n
Scientists collect data on the blood cholesterol levels(milligrams per deciliter of blood) of a random sample of 24 laboratory rats. A 95% confidence interval for the mean blood cholesterol level m is 80.2 to 89.8. Which of the following would cause the most worry about the validity of this
Watching TV (6.1, 7.3) Choose a young person (aged 19 to 25) at random and ask, “In the past seven days, how many days did you watch television?” Call the response X for short. Here is the probability distribution for X:31 Days: 0 1 2 3 4 5 6 7 Probability: 0.04 0.03 0.06 0.08 0.09 0.08 0.05
It’s critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.(a) Estimating a population proportion p at a 94% confidence level based on an SRS of size 125.(b) Estimating a population mean m at a 99% confidence level based on an SRS of
Batteries A company that produces AA batteries tests the lifetime of a random sample of 30 batteries using a special device designed to imitate real-world use. Based on the testing, the company makes the following statement: “Our AA batteries last an average of 430 to 470 minutes, and our
We love football! A recent Gallup Poll conducted telephone interviews with a random sample of adults aged 18 and older. Data were obtained for 1000 people. Of these, 37% said that football is their favorite sport to watch on television.(a) Define the parameter p in this setting. Explain to someone
Smart kids A school counselor wants to know how smart the students in her school are. She gets funding from the principal to give an IQ test to an SRS of 60 of the over 1000 students in the school. The mean IQ score was 114.98 and the standard deviation was 14.80.34(a) Define the parameter m in
Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that
Running red lights A random digit dialing telephone survey of 880 drivers asked, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?”Of the 880 respondents, 171 admitted that at least one light had been red.35(a) Construct and
Engine parts Here are measurements (in millimeters)of a critical dimension on an SRS of 16 of the more than 200 auto engine crankshafts produced in one day:224.120 224.001 224.017 223.982 223.989 223.961 223.960 224.089 223.987 223.976 223.902 223.980 224.098 224.057 223.913 223.999(a) Construct
Good wood? A lab supply company sells pieces of Douglas fir 4 inches long and 1.5 inches square for force experiments in science classes.From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000 pounds. You want to estimate the mean load needed
It’s about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.(a) Increasing the confidence level(b) Quadrupling the sample size
t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.(a) When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for
The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that(a) 95% of all Gallup Poll samples like this one give answers
The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is(a) 190. (b) 27.84. (c) 22.73. (d) 16.07. (e) 13.13.
In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size 24 from the population?(a) A stemplot of the data
T8.4 Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers
You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is(a) 1.645. (b) 1.699. (c) 1.697. (d) 1.96. (e) 2.045.
A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to
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