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intro stats

Questions and Answers of Intro Stats

Golf drives III 2013 In Chapter 3 we looked at distance that 155 professional golfers drove the ball (in yds) during a week in 2013. Here is a histogram of those drives
Braking A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer tread life. The
Maze Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to
Yogurt Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:130 160 150 120 120 110 170 160 110 130 9a) Check the assumptions and conditions for
Chips Ahoy! In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,”claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000
Ski wax Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course
Popcorn Yvon Hopps ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with
Doritos Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7,
Ruffles Students investigating the packaging of potato chips purchased 6 bags of Lay’s Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the
Saving gas Congress regulates corporate fuel economy and sets an annual gas mileage for cars.A company with a large fleet of cars hopes to meet the goal of 32.6 mpg or better for their fleet of
Marriage In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years.It is widely suspected that young people today are waiting longer to get married.
Computer lab fees The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate
Fuel economy 2014 revisited In Chapter 6, we examined the average fuel economy of several 2014 model vehicles.a) Find and interpret a 95% confidence interval for the gas mileage of 2014 vehicles.b)
Golf balls The United States Golf Association (USGA)sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an
Pizza A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.09. Explain in this
Hot dogs A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for “reduced sodium” franks. The lab failed to reject the
Farmed salmon, second look This chapter’s For Examples looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992
Flight on time 2013 revisited Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were delayed each month from
Flight on time 2013 What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline
Better light After his first attempt to determine the speed of light (described in Exercise 27), Michelson conducted an“improved” experiment. In 1897, he reported results of 100 trials with a
Speed of light In 1882, Michelson measured the speed of light (usually denoted c as in Einstein’s famous equation E = mc2). His values are in km/sec and have 299,000 subtracted from them. He
Parking II Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.a) Someone suggests that the city use its data to
Normal temperatures, part II Consider again the statistics about human body temperature in Exercise 23.a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval you
Parking Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a
Normal temperature The researcher described in Exercise 19 also measured the body temperatures of that randomly selected group of adults. Here are summaries of the data he collected. We wish to
Credit card charges A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. Here’s a histogram.A computer program found that the
CEO compensation A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. Here’s a
Crawling Data collected by child development scientists produced this confidence interval for the average age(in weeks) at which babies begin to crawl:a) Explain carefully what the software output
Pulse rates 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:a) Explain
Snow Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23", with a margin of error of {2 inches. Assuming he
Meal plan After surveying students at Dartmouth College, a campus organization calculated that a 95%confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester
Teachers Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct?What’s wrong with the others?a) If we
Cattle Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence
A good book An English professor is attempting to estimate the mean number of novels that the student body reads during their time in college. He is conducting an exit survey with seniors. He hopes
Jelly A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He needs to collect enough data to construct a confidence interval
Home prices II Suppose the standard deviation of home price losses had been $3000, as in Exercise 8? What would your conclusion be then?
Home prices The last census of the entire community from which the sample in Exercise 7 was taken was 2010 when the mean loss was $10,200. From the sample in Exercise 7, use a t-test to test whether
t-models, last time Using the t tables, software, or a calculator, estimatea) the P-value for t … 2.19 with 41 degrees of freedom.b) the P-value for • t • 7 2.33 with 12 degrees of freedom.
t-models, again Using the t tables, software, or a calculator, estimatea) the P-value for t Ú 1.69 with 6 degrees of freedom.b) the P-value for • t • 7 1.89 with 24 degrees of freedom.
Home sales again In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value.a) Suppose the standard deviation of the losses had been $3000 instead of
Home sales The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average
t-models, part IV Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
t-models, part III Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
t-models, part II Using the t tables, software, or a calculator, estimatea) the critical value of t for a 99% confidence interval with df = 2.b) the critical value of t for a 90% confidence interval
t-models, part I Using the t tables, software, or a calculator, estimatea) the critical value of t for a 99% confidence interval with df = 12.b) the critical value of t for a 98% confidence interval
LSAT The LSAT (a test taken for law school admission)has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches
Salmon A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 37 pounds with a standard deviation of 4 pounds. The company ships them to restaurants
Let’s build a 90% confidence interval for the mean amount that college students sleep in a night.Question: What can we say about the mean amount of sleep that college students get?
Based on weighing thousands of animals, the American Angus Association reports that mature Angus cows have a mean weight of 1309 pounds with a standard deviation of 157 pounds. This result was based
AP Stats The College Board reported that 57.9% of all students who took the 2013 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She
John Wayne Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955, Wayne was in Utah shooting the film The Conqueror.Across the state line, in Nevada, the
TV ads A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high
Lost luggage An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 89% is recovered and
Acid rain A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the
Dropouts Some people are concerned that new tougher standards and high-stakes tests adopted in many states have driven up the high school dropout rate. The National Center for Education Statistics
Jury Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent
Women executives A company is criticized because only 15 of 40 people in executive-level positions are women.The company explains that although this proportion is lower than it might wish, it’s not
Seeds A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The
WebZine A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine
Football 2013 During the 2013 season, the home team won 153 of the 245 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test
Twins A national vital statistics report indicated that about 2.5% of all births produced twins. Is the rate of twin births the same among very young mothers? Data from a large city hospital found
Scratch and dent An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the
Pollution A company with a fleet of 150 cars found that the emissions systems of 2 out of the 23 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 25% of
Med school 2013 According to the Association of American Medical Colleges, only 42% of medical school applicants were admitted to a medical school in the fall of 2013.6 Upon hearing this, the
Law school 2011 According to the Law School Admission Council, in the fall of 2011, 71% of law school applicants were accepted to some law school.5 The training program LSATisfaction claims that 174
Take the offer, part II In Exercise 24 of Chapter 8, you learned that First USA, a major credit card company, is planning a new offer for their current cardholders. First USA will give double airline
Contributions, please, part II In Exercise 23 of Chapter 8, you learned that the Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing
Educated mothers The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess
Absentees The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In
Abnormalities In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in
Dowsing In a rural area, only about 16% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by“dowsing”—using a forked
Obesity 2008 In 2008, the Centers for Disease Control and Prevention reported that 34% of adults in the United States are obese. A county health service planning a new awareness campaign polls a
Smartphones Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of
Candy Someone hands you a box with 29 chocolatecovered candies, telling you that 13 are vanilla creams and the rest are peanut butter. You pick candies at random and discover the first three you eat
He cheats? A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails. You try
Cars A survey investigating whether the proportion of today’s high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017.Is it reasonable to conclude
Relief A company’s old antacid formula provided relief for 83% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.441. Is it reasonable to
Dice The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03.
Positives After the political ad campaign described in Exercise 11, parta, pollsters check the president’s positives.They test the hypothesis that the ads produced no change against the alternative
More hypotheses Write the null and alternative hypotheses you would use to test each situation.a) In the 1950s, only about 40% of high school graduates went on to college. Has the percentage
Hypotheses Write the null and alternative hypotheses you would use to test each of the following situations:a) A president is concerned about his “positives”—the percentage of the country’s
Expensive medicine Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct
Bad medicine Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger
Hispanic origin II The county supervisor in Exercise 5 is going to perform a hypothesis test to see if she has evidence that the proportion of people in her county that are of Hispanic or Latino
Psychic again (you should have seen this coming) If you were to do a hypothesis test on your experiment with your“psychic” friend from Exercise 2, would your alternative hypothesis be one-sided
Empty houses According to the 2010 Census, 11.4%of all housing units in the United States were vacant.A county supervisor wonders if her county is different from this. She randomly selects 850
Hispanic origin According to the 2010 Census, 16% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic
Psychic after all? The “psychic” friend from Exercise 2 correctly identified more than 25% of the cards.a) A hypothesis test gave a P-value of 0.014. What do you conclude?b) What would you
Better than aspirin 2? A clinical trial compares the new drug described in Exercise 1 to aspirin. The group using the new drug had somewhat fewer heart attacks than those in the aspirin group.a) The
Psychic A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or
Better than aspirin? A very large study showed that aspirin reduced the rate of first heart attacks by 44%.A pharmaceutical company thinks they have a drug that will be more effective than aspirin,
Anyone who plays or watches sports has heard of the “home field advantage.”Tournaments in many sports are designed to try to neutralize the advantage of the home team or player. Most people
A large city’s DMV claimed that 80% of candidates pass driving tests. Data from a reporter’s survey of randomly selected local teens who had taken the test produced a P-value of 0.002.Question:
A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found
Amendment A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52% would vote in
Approval rating A newspaper reports that the governor’s approval rating stands at 60%. The article adds that the poll is based on a random sample of 1775 adults and has a margin of error of 3%.
Another pilot study During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood—a possible warning signal for diabetes.
Pilot study A state’s environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage
Better hiring info Editors of the business report in Exercise 38 are willing to accept a margin of error of 4% but want 99% confidence. How many randomly selected employers will they need to contact?
Graduation, again As in Exercise 37, we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level

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