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elementary statistics

Questions and Answers of Elementary Statistics

Coke Volumes Data Set 17 in Appendix B includes the volumes (in ounces) of the regular Coke in a sample of 36 different cans that are all labeled 12 oz. A line manager claims that the mean amount of
Tobacco Use in Children’s Movies Refer to Data Set 7 in Appendix B and use only those movies that show some use of tobacco. Test the claim of a movie critic that“among those movies that show the
Tom Clancy Reading Level Refer to Data Set 14 in Appendix B and use the FleschKincaid Grade Level measurements for The Bear and the Dragon by Tom Clancy. A high school teacher wants to assign the
Nicotine in Cigarettes The Carolina Tobacco Company advertised that its bestselling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly
Olympic Winners Listed below are the winning times (in seconds) of men in the 100-meter dash for consecutive summer Olympic games, listed in order by row. Assuming that these results are sample data
Treating Chronic Fatigue Syndrome Patients with chronic fatigue syndrome were tested, then retested after being treated with fludrocortisone. Listed below are the changes in fatigue after the
Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter or mg m3) in the air. The Environmental Protection Agency has established an air quality standard for
Pulse Rates The author, at the peak of an exercise program, claimed that his pulse rate was lower than the mean pulse rate of statistics students. The author’s pulse rate was measured to be 60
Effect of Vitamin Supplement on Birth Weight The birth weights (in kilograms) are recorded for a sample of male babies born to mothers taking a special vitamin supplement (based on data from the New
Reliability of Aircraft Radios The mean time between failures (in hours) for a Telektronic Company radio used in light aircraft is 420 h. After 15 new radios were modified in an attempt to improve
BMW Crash Tests Because of the expense involved, car crash tests often use small samples. When five BMW cars are crashed under standard conditions, the repair costs (in dollars) are used to test the
Baseballs In previous tests, baseballs were dropped 24 ft onto a concrete surface, and they bounced an average of 92.84 in. In a test of a sample of 40 new balls, the bounce heights had a mean of
Conductor Life Span A New York Times article noted that the mean life span for 35 male symphony conductors was 73.4 years, in contrast to the mean of 69.5 years for males in the general population.
Textbook Prices Heather Carielli is a former student of the author who earned a Master’s degree in statistics at the University of Massachusetts. When she randomly selected 16 new textbooks in the
Testing Wristwatch Accuracy Students of the author randomly selected 40 people and measured the accuracy of their wristwatches, with positive errors representing watches that are ahead of the correct
Heights of Parents Data Set 2 in Appendix B includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother’s height from the
Actual and Forecast Temperatures Data Set 10 in Appendix B includes a list of actual high temperatures and the corresponding list of three-day forecast high temperatures.If the difference for each
Sugar in Cereal Data Set 16 in Appendix B lists the sugar content (grams of sugar per gram of cereal) for a sample of different cereals. Those amounts are summarized with these statistics: n 5 16, 5
Harry Potter and Reading Level Data Set 14 in Appendix B lists measured reading levels for 12 pages randomly selected from J. K. Rowling’s Harry Potter and the Sorcerer’s Stone. The
Testing the Assumed s In the example included in this section, we rejected H0: m 5 98.6 and supported H1: m 2 98.6 given the assumption that s 5 0.62 and the sample data consist of n 5 106 values
Are Thinner Aluminum Cans Weaker? Data Set 20 in Appendix B includes the measured axial loads (in pounds) of 175 cola cans that use aluminum 0.0109 in. thick. Before obtaining these sample results,
Differences Between Forecast and Actual High Temperatures Data Set 10 in Appendix B lists the actual high temperatures and the three-day forecast high temperatures. One way to investigate the
Analysis of Last Digits Analysis of the last digits of sample data values sometimes reveals whether the data have been accurately measured and reported. When single digits 0 through 9 are randomly
Probability of Type II Error For a hypothesis test with a specified significance levela, the probability of a type I error isa, whereas the probability b of a type II error depends on the particular
False Claim A researcher claimed that when 20 mice were treated, the success rate was equal to 47%. What is the basis for rejecting that claim?
Misleading with Statistics Chemco, a supplier of chemical-waste containers, finds that 3% of a sample of 500 units are defective. Being fundamentally dishonest, the Chemco production manager wants to
Coping with No Successes In a simple random sample of 50 plain M&M candies, it is found that none of them are blue. We want to use a 0.01 significance level to test the claim of Mars, Inc., that the
Alternative Method of Testing a Claim About p In a study of perception, 80 men are tested and 7 are found to have red green color blindness (based on data from USA Today). We want to use a 0.01
Proving Claims In the USA Today article “Power Lines Not a Cancer Risk for Kids,”the first sentence states that “Children who live near high voltage power lines appear to be no more likely to
Using the Continuity Correction Repeat Exercise 20, but include the correction for continuity that was described in Section 5-6. How are the results affected by including the continuity correction?
Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits
Alcohol and Tobacco Use in Animated Children’s Movies Using results listed in Data Set 7 in Appendix B, test the claim that the majority of animated children’s movies show the use of alcohol or
Using M&M Data Refer to Data Set 19 in Appendix B and find the sample proportion of M&Ms that are blue. Use that result to test the claim of Mars, Inc., that 10% of its plain M&M candies are blue.
Interpreting Calculator Display A television executive claims that “fewer than half of all adults are annoyed by the violence shown on television.” Sample data from a Roper poll showed that 48%
Interpreting Calculator Display The Federal Aviation Administration will fund research on spatial disorientation of pilots if there is sufficient sample evidence (at the 0.01 significance level) to
TV Ratings A simple random sample of households with TV sets in use shows that 1024 of them were tuned to 60 Minutes while 3836 were tuned to some other show.Use a 0.025 significance level to test
Smoking and College Education One survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke and 641 do not smoke (based on data from the American Medical
Testing Effectiveness of Nicotine Patches In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year
Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as
Testing Lipitor for Cholesterol Reduction In clinical tests of the drug Lipitor (generic name, atorvastatin), 863 patients were treated with 10 mg doses of atorvastatin, and 19 of those patients
Umpire Strike Rate In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61.0% called the previous year. At one point in the
Drug Testing of Job Applicants In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 significance level, test the claim that the failure rate is now lower if a simple
Store Checkout-Scanner Accuracy In a study of store checkout-scanners, 1234 items were checked and 20 of them were found to be overcharges (based on data from“UPC Scanner Pricing Systems: Are They
Cloning Survey In a Gallup poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. Use a 0.05 significance level to test the claim that less than 10% of all adults
Photo-Cop Legislation The Chapter Problem included this question: “Is there sufficient sample evidence to support a claim that the proportion of all adult Minnesotans opposed to photo-cop
Percentage of Telephone Users A recent survey of 4276 randomly selected households showed that 4019 of them had telephones (based on data from the U.S. Census Bureau). Use those survey results to
Percentage of E-Mail Users Technology is dramatically changing the way we communicate. In 1997, a survey of 880 U.S. households showed that 149 of them use e-mail (based on data from The World
Federal Drug Offenses In a recent year, of the 109,857 arrests for Federal offenses, 29.1% were for drug offenses (based on data from the U.S. Department of Justice).Use a 0.01 significance level to
Glamour Magazine Survey Glamour magazine sponsored a survey of 2500 prospective brides and found that 60% of them spent less than $750 on their wedding gown.Use a 0.01 significance level to test the
Survey of Drinking In a Gallup survey, 1087 randomly selected adults were asked“Do you have occasion to use alcoholic beverages such as liquor, wine, or beer, or are you a total abstainer?”
Mendel’s Hybridization Experiments In one of Mendel’s famous hybridization experiments, 8023 offspring peas were obtained, and 24.94% of them had green flowers. The others had white flowers.
Power of a Test Assume that you are using a significance level of a 5 0.05 to test the claim that p , 0.5 and that your sample is a simple random sample of size n 5 1998 with 5 0.48.a. Findb, the
Why Not Let a 5 0? Someone suggests that in testing hypotheses, you can eliminate a type I error by making a 5 0. In a two-tailed test, what critical values correspond to a 5 0? If a 5 0, will the
Proving Claims You are the quality control manager at Mars, Inc., and you want to prove the company’s claim that 10% of all M&M candies are blue. Is it possible to prove that claim using methods of
P-Value Assume that you have just developed a new manufacturing process that you believe reduces the rate of defects when microchips are produced. You plan to justify your claim of a lower rate of
Significance Level If a null hypothesis is rejected with a significance level of 0.05, is it also rejected with a significance level of 0.01? Why or why not?
Unnecessary Test When testing a claim that the majority of adult Americans are against the death penalty for a person convicted of murder, a random sample of 491 adults is obtained, and 27% of them
Alcohol Service Policy: Determining Sample Size In a Gallup poll of 1004 adults, 93% indicated that restaurants and bars should refuse service to patrons who have had too much to drink. If you plan
Determining Sample Size You want to estimate the percentage of U.S. statistics students who get grades of B or higher. How many such students must you survey if you want 97% confidence that the
Estimating Variation Data Set 14 in Appendix B includes the Flesch-Kincaid Grade Level ratings for 12 pages randomly selected from J. K. Rowlings’s Harry Potter and the Sorcerer’s Stone, and
Estimating Ease of Reading Data Set 14 in Appendix B includes Flesch-Kincaid Grade Level ratings for works by Tom Clancy, J. K. Rowling, and Leo Tolstoy. If you want to estimate the mean
Estimates of Ease of Reading Refer to Data Set 14 for the Flesch-Kincaid Grade Level ratings for 12 randomly selected pages taken from books by Tom Clancy, J. K.Rowling, and Leo Tolstoy.a. Construct
Estimates from Voter Surveys In a recent presidential election, 611 voters were surveyed and 308 of them said that they voted for the candidate who won (based on data from the ICR Survey Research
Estimating Length of Car Ownership A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A simple random sample of 25 car owners results in 5 7.01 years and
Estimating Theme Park Attendance Each year, billions of dollars are spent at theme parks owned by Disney, Universal Studios, Sea World, Busch Gardens, and others. A survey of 1233 people who took
Finding Critical Values In constructing confidence intervals for s or s2, we use Table A-4 to find the critical values and , but that table applies only to cases in which n # 101, so the number of
Finding Missing Data A journal article includes a graph showing that sample data are normally distributed.a. The confidence level is inadvertently omitted when this confidence interval is given: 2.8
Body Mass Index Refer to Data Set 1 in Appendix B and use the sample data.a. Construct a 99% confidence interval estimate of the standard deviation of body mass indexes for men.b. Construct a 99%
a. Comparing Waiting Lines The listed values are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows.
Pulse Rates A medical researcher wants to determine whether male pulse rates vary more or less than female pulse rates. Using the sample pulse rates in Data Set 1 in Appendix B, the male pulse rates
Shoveling Heart Rates Because cardiac deaths appear to increase after heavy snowfalls, an experiment was designed to compare cardiac demands of snow shoveling to those of using an electric snow
Quality Control of Doughnuts The Hudson Valley Bakery makes doughnuts that are packaged in boxes with labels stating that there are 12 doughnuts weighing a total of 42 oz. If the variation among the
Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter or mg m3) in the air. The Environmental Protection Agency has established an air quality standard for
Car Antifreeze A container of car antifreeze is supposed to hold 3785 mL of the liquid. Realizing that fluctuations are inevitable, the quality-control manager wants to be quite sure that the
Destroying Dodge Vipers With destructive testing, sample items are destroyed in the process of testing them. Crash testing of cars is one very expensive example of destructive testing. Twelve Dodge
Confidence Interval for Sample of Size n 5 1 When a lone alien lands on earth, he is measured and is found to have a height of 3.2 ft. It is reasonable to expect that the height of all such aliens
Effects of Units of Measurement A confidence interval is constructed for a small simple random sample of temperatures (in degrees Fahrenheit) selected from a normally distributed population for which
Using the Wrong Distribution Assume that a small simple random sample is selected from a normally distributed population for which s is unknown. Construction of a confidence interval should use the t
Effect of an Outlier Test the effect of an outlier as follows: Use the sample data from Exercise 17 to find a 95% confidence interval estimate of the population mean, after changing the first value
Body Mass Index Refer to Data Set 1 in Appendix B and use the sample data.a. Construct a 99% confidence interval estimate of the mean body mass index for men.b. Construct a 99% confidence interval
Comparing Regular and Diet Pepsi Refer to Data Set 17 in Appendix B and use the sample data.a. Construct a 95% confidence interval estimate of the mean weight of cola in cans of regular Pepsi.b.
Head Circumferences In order to correctly diagnose the disorder of hydrocephalus, a pediatrician investigates head circumferences of two-year-old males and females. Use the sample data from Data Set
Skull Breadths Maximum breadth of samples of male Egyptian skulls from 4000 B.C.and 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver):4000 B.C.: 131 119 138
Pulse Rates A physician wants to develop criteria for determining whether a patient’s pulse rate is atypical, and she wants to determine whether there are significant differences between males and
Shoveling Heart Rates Because cardiac deaths appear to increase after heavy snowfalls, an experiment was designed to compare cardiac demands of snow shoveling to those of using an electric snow
Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter or mg m3) in the air. The Environmental Protection Agency has established an air quality standard for
Estimating Car Pollution In a sample of seven cars, each car was tested for nitrogenoxide emissions (in grams per mile) and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08,
Heights of Parents Data Set 2 in Appendix B includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother’s height from the
Forecast and Actual Temperatures Data Set 10 in Appendix B includes a list of actual high temperatures and the corresponding list of three-day forecast high temperatures.If the difference for each
Crash Hospital Costs A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with
Sample Size Using Sample Data You want to estimate the mean diastolic blood pressure level of adult females. Refer to Data Set 1 in Appendix B and find the maximum and minimum diastolic blood
Sample Size Using Sample Data You want to estimate the mean pulse rate of adult males. Refer to Data Set 1 in Appendix B and find the maximum and minimum pulse rates for males, then use those values
Sample Size Using Range Rule of Thumb Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb to estimate the standard
Sample Size Using Range Rule of Thumb You have just been hired by the marketing division of General Motors to estimate the mean amount of money now being spent on the purchase of new cars in the
Sample Size for Television Viewing Nielsen Media Research wants to estimate the mean amount of time (in minutes) that full-time college students spend watching television each weekday. Find the
Sample Size for Estimating Income An economist wants to estimate the mean income for the first year of work for college graduates who have had the profound wisdom to take a statistics course. How
Sample Size for Weights of Quarters The Tyco Video Game Corporation finds that it is losing income because of slugs used in its video games. The machines must be adjusted to accept coins only if they
Sample Size for Mean IQ of Statistics Students The Weschler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size
Head Circumferences In order to help identify baby growth patterns that are unusual, we need to construct a confidence interval estimate of the mean head circumference of all babies that are two
Cotinine Levels of Smokers When people smoke, the nicotine they absorb is converted to cotinine, which can be measured. A sample of 40 smokers has a mean cotinine level of 172.5. Assuming that s is

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