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elementary statistics
Elementary Statistics 9th Edition Mario F. Triola - Solutions
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 regular Coke is greater than 12 oz, causing lower company profits. Using a 0.01 significance level,
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 use of tobacco, the mean exposure time is 2 minutes.” Given the sample data, is that claim
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 book for a reading assignment, but he requires a book with a reading level above grade 6. Is there
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 selected cigarettes and found the amounts (in mg) shown in the accompanying list. It’s a serious
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 randomly selected from the population of all past and future Olympic games, test the claim that the
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 treatment (based on data from “The Relationship Between Neurally Mediated Hypotension and the Chronic
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 lead: 1.5 mg m3. The measurements shown below were recorded at Building 5 of the World Trade Center
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 beats per minute, and the 20 students in his class measured their pulse rates. When testing the claim
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 York State Department of Health). When testing the claim that the mean birth weight for all male
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 reliability, tests were conducted to measure the times between failures. When Minitab is used to test
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 claim that the mean repair cost for all BMW cars is less than $1000. The Minitab results of this
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 92.67 in. and a standard deviation of 1.79 in. (based on data from Brookhaven National Laboratory and
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. Assuming that the 35 males have life spans with a standard deviation of 8.7 years, use a 0.05
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 college bookstore, she found that they had prices with a mean of $70.41 and a standard deviation of
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 time and negative errors representing watches that are behind the correct time. The 40 values have
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 father’s height, the result is a list of 20 values with a mean of 4.4 in. and a standard deviation of
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 day is found by subtracting the three-day forecast high temperature from the actual high temperature,
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 0.295 g, s 5 0.168 g. Use a 0.05 significance level to test the claim of a cereal lobbyist that the
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 Flesch-Kincaid Grade Level measurements are summarized with these statistics: n 5 12, 5 5.075, s 5 1.168.
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 with 5 98.20.a. What aspect of this example is not realistic?b. Find the largest value of s that
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, the standard cans had a thickness of 0.0111 in.and the mean axial load was 281.81 lb. When using the
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 accuracy of those forecast temperatures is to find the differences between the actual and the forecast
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 selected with replacement, the mean should be 4.50 and the standard deviation should be 2.87. Reported
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 value of p that is used as an alternative to the null hypothesis.Refer to Exercise 20.Assuming that
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 make a claim that the rate of defective units is no more than some specified percentage, and he
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 proportion of M&M candies that are blue is equal to 0.10. Can the methods of this section be used?
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 significance level to test the claim that men have a red green color-blindness rate that is greater than
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 get leukemia than other kids, doctors report today in the most extensive study of one of the most
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 are randomly selected, the proportion of zeros should be 0.1.a. Use the traditional method with a
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 tobacco (or both). Use a 0.05 significance level.7-3 Beyond the Basics
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% of 1,998 surveyed adults indicated their annoyance with television violence. The accompanying TI-83
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 conclude that among aircraft accidents involving such disorientation, more than three-fourths result
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 the claim of a CBS executive that “60 Minutes gets more than a 20 share,” which means that more
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 Association). Use a 0.01 significance level to test the claim that the rate of smoking among those
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 after the treatment (based on data from “HighDose Nicotine Patch Therapy,” by Dale et al.,
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 reported in USA Today). Test the claim of a once popular belief that such cancers are affected by
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 experienced flu symptoms (based on data from Parke-Davis). Use a 0.01 significance level to test the
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 season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today).
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 random sample of 1520 current job applicants results in 58 failures (based on data from the
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 Accurate?” by Goodstein, Journal of Marketing, Vol. 58). Use a 0.05 significance level to test the
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 say that cloning of humans should be allowed. Can a newspaper run a headline that “less than 10% of
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 legislation is greater than 0.5?” Use a 0.10 significance level to test the claim that the proportion is
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 test the claim that the percentage of households is now greater than the 35% rate that was found in
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 Almanac and Book of Facts). Use those sample results to test the claim that more than 15% of U.S.
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 test the claim that the drug offense rate is equal to 30%. How can the result be explained, given
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 claim that less than 62% of brides spend less than $750 on their wedding gown. How are the results
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?” Sixty-two percent of the subjects said that they used alcoholic beverages. Consider a hypothesis test
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. Consider a hypothesis test that uses a 0.05 significance level to test the claim that green-flowered
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 probability of making a type II error, given that the population proportion is actually 0.45. (Hint:
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 null hypothesis ever be rejected?
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 hypothesis testing? Why or why not?
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 defects by using a hypothesis test. Which P-value would you prefer: 0.10, 0.05, 0.01? Why?
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 are against the death penalty (based on data from a Gallup poll). Find the P-value. Why is it not
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 to conduct a new poll to confirm that the percentage continues to be correct, how many randomly
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 sample percentage is off by no more than two percentage points?
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 those 12 ratings have a standard deviation of 1.17, and they appear to come from a normally distributed
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 Flesch-Kincaid Grade Level rating for pages from J. R. R.Tolkien’s Lord of the Rings, how many pages must you
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 a 95% confidence interval estimate of the mean Flesch-Kincaid Grade Level rating for the population
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 Group).a. Find the point estimate of the percentage of voters who said that they voted for the
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 s 5 3.74 years, respectively (based on data from a Roper poll). Assume that the sample is drawn from
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 trips revealed that 111 of them included a visit to a theme park (based on data from the Travel
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 degrees of freedom is 100 or fewer. For larger numbers of degrees of freedom, we can approximate and
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 , s , 6.0. Find the confidence level for these given sample statistics:.b. This 95% confidence
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% confidence interval estimate of the standard deviation of body mass indexes for women.c. Compare and
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. Construct a 95% confidence interval for the population standard deviation s.6.5 6.6 6.7 6.8 7.1 7.3 7.4
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 can be summarized with the statistics n 5 40, 5 69.4, s 5 11.3. For females, the statistics are n 5
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 thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats per
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 doughnuts is too large, some boxes will be underweight (cheating consumers) and others will be
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 lead: 1.5 mg m3. The measurements shown below were recorded at Building 5 of the World Trade Center
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 standard deviation is less than 30 mL. Otherwise, some containers would overflow while others would not
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 Viper sports cars (list price: $59,300) are crash tested under a variety of conditions that simulate
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 are normally distributed?a. The methods of this chapter require information about the variation of a
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 s is unknown.a. How is the margin of error E affected if each temperature is converted to the
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 distribution, but how are the confidence interval limits affected if the normal distribution is
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 from 0.06 grams mile to 60 grams mile. This value is not realistic, but such an error can easily
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 estimate of the mean body mass index for women.c. Compare and interpret the results. We know that men
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. Construct a 95% confidence interval estimate of the mean weight of cola in cans of diet Pepsi.c. Compare
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 3 to construct confidence intervals, then determine whether there appears to be a difference between
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.: 131 119 138 125 129 126 131 132 126 128 128 131 150 A.D.: 136 130 126 126 139 141 137 138 133 131 134 129 Changes
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 females. Using the sample pulse rates in Data Set 1 in Appendix B, the male pulse rates can be
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 thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats per
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 lead: 1.5 mg m3. The measurements shown below were recorded at Building 5 of the World Trade Center
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, 0.15 (based on data from the Environmental Protection Agency). Assuming that this sample is
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 father’s height, the result is a list of 20 values with a mean of 4.4 in. and a standard deviation of
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 day is found by subtracting the three-day forecast high temperature from the actual high temperature,
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 a mean of $9004 and a standard deviation of $5629(based on data from the U.S. Department of
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 pressure level for females, then use those values with the range rule of thumb to estimate s. How many
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 with the range rule of thumb to estimate s. How many adult males must you randomly select and test
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 deviation. Next, find the size of the sample required to estimate the mean age (in years) of textbooks
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 United States. First use the range rule of thumb to make a rough estimate of the standard deviation of
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 necessary to estimate that mean with a 15-minute margin of error. Assume that a 96%
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 many such incomes must be found if we want to be 95% confident that the sample mean is within $500 of
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 fall within set limits. In order to set those limits, the mean weight of quarters in circulation
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 necessary to estimate the mean IQ score of statistics students. We want to be 95% confident that our
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 months old. A random sample of 100 babies is obtained, and the mean head circumference is found to be
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 known to be 119.5, find a 90% confidence interval estimate of the mean cotinine level of all smokers.
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