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intro stats

Questions and Answers of Intro Stats

Bread Clarksburg Bakery is trying to predict how many loaves to bake. In the past 100 days, the bakery has sold between 95 and 140 loaves per day. Here are a histogram and the summary statistics for
Skin cancer In February 2012, MedPage Today reported that researchers used vemurafenib to treat metastatic melanoma (skin cancer). Out of 152 patients, 53% had a partial or complete response to
Streams Researchers in the Adirondack Mountains collect data on a random sample of streams each year.One of the variables recorded is the substrate of the stream—the type of soil and rock over
Occupy Wall Street In 2011, the Occupy Wall Street movement protested the concentration of wealth and power in the United States. A 2012 University of Delaware survey asked a random sample of 901
Meals A college student is on a “meal program.” His budget allows him to spend an average of $10 per day for the semester. He keeps track of his daily food expenses for 2 weeks; the data are
Petitions To get a voter initiative on a state ballot, petitions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The board then has 60 days to
Speeding A newspaper report in August 2002 raised the issue of racial bias in the issuance of speeding tickets.The following facts were noted:■ Sixteen percent of drivers registered in New Jersey
Women The U.S. Census Bureau reports that 26% of all U.S. businesses are owned by women. A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of
Dropouts One study comparing various treatments for the eating disorder anorexia nervosa initially enlisted 198 subjects, but found overall that 105 failed to complete their assigned treatment
Name recognition, part II The advertising company described in Exercise 31 is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her.a) Fans
Name recognition An advertising agency won’t sign an athlete to do product endorsements unless it is sure the person is known to more than 25% of its target audience.The agency always conducts a
Grade inflation In 1996, 20% of the students at a major university had an overall grade point average of 3.5 or higher (on a scale of 4.0). In 2012, a random sample of 1100 student records found that
Approval 2008 Of all the post–World War II presidents, Richard Nixon had the highest disapproval rating near the end of his presidency. His disapproval rating peaked at 66% in July 1974, just
Power We are replicating an experiment. How will each of the following changes affect the power of our test?Indicate whether it will increase, decrease, or remain the same, assuming that all other
Fried PCs A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another
Safety Observers in Texas watched children at play in eight communities. Of the 814 children seen biking, roller skating, or skateboarding, only 14% wore a helmet.a) Create and interpret a 95%
Errors An auto parts company advertises that its special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs.” An independent laboratory decides to test part of
Alcohol abuse Growing concern about binge drinking among college students has prompted one large state university to conduct a survey to assess the size of the problem on its campus. The university
Teen smoking 2009 The Centers for Disease Control and Prevention say that about 19.5% of teenagers smoke tobacco (down from a high of 38% in 1997). A college has 522 students in its freshman class.
Church going In December 2011, Pew Research found that 921 American adults out of 2303 surveyed are active in a church, religious, or spiritual organization.a) Create a 95% confidence interval for
Cigarettes 2009 In 1999, the Centers for Disease Control and Prevention estimated that about 34.8% of high school students smoked cigarettes. They established a national health goal of reducing that
Language Neurological research has shown that in about 80% of people language abilities reside in the brain’s left side. Another 10% display right-brain language centers, and the remaining 10% have
Cheating A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had
Largemouth bass Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the
Teen deaths 2005 Traffic accidents are the leading cause of death among people aged 16 to 20. In May 2005, the National Highway Traffic Safety Administration reported that even though only 6.3% of
Enough eggs? One of the important issues for poultry farmers is the production rate—the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day),
Polling disclaimer A newspaper article that reported the results of an election poll included the following explanation:The Associated Press poll on the 2012 presidential campaign is based on
Eggs The ISA Babcock Company supplies poultry farmers with hens, advertising that a mature B300 Layer produces eggs with a mean weight of 60.7 grams.Suppose that egg weights follow a Normal model
Archery A champion archer can generally hit the bull’s-eye 80% of the time. Suppose she shoots 200 arrows during competition. Let pn represent the percentage of bull’s-eyes she gets (the sample
Vitamin D 2012 In 2012, the American Journal of Clinical Nutrition reported that 31% of Australian adults over age 25 have a vitamin D deficiency. The data came from the AusDiab study of 11,218
Bimodal We are sampling randomly from a distribution known to be bimodal.a) As our sample size increases, what’s the expected shape of the sample’s distribution?b) What’s the expected value of
Gay marriage In February 2014, Pew Research asked a random sample of 1821 U.S. adults, “Do you strongly favor, favor, oppose, or strongly oppose allowing gays and lesbians to marry legally?”
Net-Newsers In June 2008, the Pew Research Foundation sampled 3615 U.S. adults and asked about their choice of news sources. They identified 13% as“Net-Newsers” who regularly get their news from
Dice When one die is rolled, the number of spots showing has a mean of 3.5 and a standard deviation of 1.7. Suppose you roll 10 dice. What’s the approximate probability that your total is between
Scrabble Using a computer to play many simulated games of Scrabble, researcher Charles Robinove found that the letter “A” occurred in 54% of the hands. This study had a margin of error of {10%.
Babies The National Perinatal Statistics Unit of the Sydney Children’s Hospital reports that the mean birth weight of all babies born in birth centers in Australia in 2002 was 3564 grams—about
Leaky gas tanks Nationwide, it is estimated that 40%of service stations have gas tanks that leak to some extent. California is trying to lessen the prevalence of these leaks. We want to assess the
Polling 2004 The 2004 U.S. presidential election was the last presidential election that had a significant third-party candidate. The official results showed that George W.Bush received 50.7% of the
Hamsters How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.a) Create and
Color-blind Medical literature says that about 8% of males are color-blind. A university’s introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males.
Crohn’s disease Omega-3 fatty acids have been tested as a means to prevent relapse of Crohn’s disease. Two large, randomized, placebo-controlled studies have shown no such benefit from omega-3
Pottery An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. About 40% break in the kiln during firing. Hoping to
Hoops A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 55% to 75%. Dubious, the coach asks him
Faulty or not? You are in charge of shipping computers to customers. You learn that a RAM chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All
Two coins In a drawer are two coins. They look the same, but one coin produces heads 84% of the time when spun while the other one produces heads only 28% of the time. You select one of the coins.
Catheters, again The catheter company in Exercise 44 is reviewing its testing procedure.a) Suppose the significance level is changed to a = 0.01. Will the probability of a Type II error increase,
TV safety, revisited The manufacturer of the metal TV stands in Exercise 43 is thinking of revising its safety test.a) If the company’s lawyers are worried about being sued for selling an unsafe
Catheters During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that
TV safety The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company’s
Testing the ads The company in Exercise 40 contacts 600 people selected at random, and only 133 remember the ad.a) Should the company renew the contract? Support your recommendation with an
Software, part II 203 students signed up for the Stats course in Exercise 39. They used the software suggested by the salesman, and scored an average of 108 points on the final with a standard
Ads A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the
Software for learning A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics
Stop signs Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and
Equal opportunity? A company is sued for job discrimination because only 11% of the newly hired candidates were minorities when 19% of all applicants were minorities.Is this strong evidence that the
Production Consider again the task of the quality control inspectors in Exercise 34.a) In this context, what is meant by the power of the test the inspectors conduct?b) They are currently testing 5
Cars, again As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.a) In this context, what is meant by the
Quality control Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items
Testing cars A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet
Alzheimer’s Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a
Homeowners 2013 In 2013, the U.S. Census Bureau reported that 65% of American families owned their homes—the lowest rate in 18 years. Census data reveal that the ownership rate in one small city is
More spam Consider again the points-based spam filter described in Exercise 28. When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects
Second loan Exercise 27 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial
Spam Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the
Loans Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the
Fans A survey of 81 randomly selected people standing in line to enter a football game found that 73 of them were home team fans.a) Explain why we cannot use this information to construct a
Dogs Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months.A veterinarian checked 42 puppies whose
Hard times In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com)a) Estimate the true percentage of men that are taking
Approval 2014 In March 2014, Barack Obama’s approval rating stood at 40% in Gallup’s daily tracking poll of 1500 randomly surveyed U.S. adults.
Is the Euro fair? Soon after the Euro was introduced as currency in Europe, it was widely reported that someone had spun a Euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis
Groceries In January 2011, Yahoo surveyed 2400 U.S.men. 1224 of the men identified themselves as the primary grocery shopper in their household.a) Estimate the percentage of all American males who
Significant again? A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher
Significant? Public health officials believe that 90.6% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more
Alpha, again Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near
Alpha A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner.He made this decision based on a test
Another P-value Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared
P-value A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the P-value of 0.027 means in
Which alternative? In each of the following situations, is the alternative hypothesis one-sided or two-sided?What are the hypotheses?a) A college dining service conducts a survey to see if students
One sided or two? In each of the following situations, is the alternative hypothesis one-sided or two-sided? What are the hypotheses?a) A business student conducts a taste test to see whether
More errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made.a) A test of H0: m = 25 vs. HA: m 7 25 rejects the null hypothesis. Later it is
Errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.a) A bank wants to know if the enrollment on their website is above 30%
More critical values For each of the following situations, find the critical value for z or t.a) H0: m = 106 vs. HA: m 106 at a = 0.05; n = 81.b) H0: p = 0.08 vs. HA: p 7 0.08 at a = 0.10.c) H0: p
Critical values For each of the following situations, find the critical value(s) for z or t.a) H0: p = 0.5 vs. HA: p 0.5 at a = 0.05.b) H0: p = 0.4 vs. HA: p 7 0.4 at a = 0.05.c) H0: m = 10 vs. HA:
Alpha false and true Which of the following statements are true? If false, explain briefly.a) It is better to use an alpha level of 0.05 than an alpha level of 0.01.b) If we use an alpha level of
Alpha true and false Which of the following statements are true? If false, explain briefly.a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis.b) The alpha
More hypotheses For each of the following, write out the alternative hypothesis, being sure to indicate whether it is one-sided or two-sided.a) Consumer Reports discovered that 20% of a certain
Hypotheses For each of the following, write out the null and alternative hypotheses, being sure to state whether the alternative is one-sided or two-sided.a) A company reports that last year, 40% of
More P-values Which of the following are true? If false, explain briefly.a) A very low P-value provides evidence against the null hypothesis.b) A high P-value is strong evidence in favor of the null
P-values Which of the following are true? If false, explain briefly.a) A very high P-value is strong evidence that the null hypothesis is false.b) A very low P-value proves that the null hypothesis
Hypotheses and parameters As in Exercise 1, for each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.a) Seat-belt
Parameters and hypotheses For each of the following situations, define the parameter (proportion or mean)and write the null and alternative hypotheses in terms of parameter values. Example: We want
The study of Avandia published in the NEJM combined results from 47 different trials—a method called meta-analysis. The drug’s manufacturer, GlaxoSmithKline(GSK), issued a statement that pointed
A published study found the risk of heart attack to be increased in patients taking the diabetes drug Avandia. The issue of the New England Journal of Medicine(NEJM ) in which that study appeared
The baseline seven-year risk of heart attacks for diabetics is 20.2%. A NEJM study reported a 95% confidence interval equivalent to 20.8% to 40.0% for the risk among patients taking the diabetes drug
Surgeons examined their results to compare two methods for a surgical procedure used to alleviate pain on the outside of the wrist. A new method was compared with the traditional “freehand”
Motor vehicle crashes are a leading cause of death for people between 4 and 33 years old. In the past 10 years motor vehicle accidents have claimed the lives of over 40,000 people a year in the
The question of whether the diabetes drug Avandia increased the risk of heart attack was raised by a study in the New England Journal of Medicine. This study estimated the seven-year risk of heart
A New England Journal of Medicine paper reported that the seven-year risk of heart attack in diabetes patients taking the drug Avandia was increased from the baseline of 20.2% to an estimated risk of
The diabetes drug Avandia® was approved to treat Type 2 diabetes in 1999. But an article in the New England Journal of Medicine (NEJM)1 raised concerns that the drug might carry an increased risk of
Wind power Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual

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