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Elementary Statistics 10th Edition Mario F. Triola - Solutions

10. Minting Quarters Quarters are currently minted with weights having a mean of 5.670 g and a standard deviation of 0.062 g. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 24 quarters is x2 x R 5 228.9638.d 2 L 5 152.8222 x 5 2700 s
9. Birth Weights Astudy was conducted of babies born to mothers who use cocaine during pregnancy, and the following sample data were obtained for weights at birth: n 5 190, g, s 5 645 g (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et
4. Standard Deviation and Variance Is a test of the claim that s 5 2.00 equivalent to a test of the claim that s2 5 4.00? When testing the claim that s 5 2.00, do you use a different test statistic than the one used for testing the claim that s2 5 4.00?Finding Test Components. In Exercises 5–8,
3. Requirements When rolling a fair die, the results have mean m 5 3.5 and standard deviation A die is rolled 100 times in an attempt to verify that it behaves like a fair die. If you calculate the standard deviation of the 100 outcomes, can you use that value with the methods of this section to
2. Using Confidence Interval Assume that you must use a 0.01 significance level to test the claim that s . 5.00. If you plan to test that claim by constructing a confidence interval, what level of confidence should be used for the confidence interval? Will the conclusion based on the confidence
1. Robust What does it mean when we say that the chi-square test of this section is not robust against departures from normality? How does that affect the conditions that must be satisfied for the chi-square test of this section?
37. Power of a Test Refer to the sample data in Exercise 27 and assume that you’re using a 0.05 significance level for testing the claim that m , 1.8 g. Minitab is used to find that b 5 0.5873, given that the actual mean is 1.7 g. Find the power of the test and the probability of a type II error.
36. Finding Critical t Values When finding critical values, we sometimes need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating where df 5 n 2 1, e 52.718, and z is the critical z score. Use this approximation to find
35. Effect of an Outlier Repeat Exercise 25 after changing the first value from 5.40 to 540. Based on the results, describe the effect of an outlier on a t test.
34. Using the Wrong Distribution When testing a claim about a population mean with a simple random sample selected from a normally distributed population with unknown s, the Student t distribution should be used for finding critical values and or a P-value. If the standard normal distribution is
33. Alternative Method When testing a claim about the population mean m using a simple random sample from a normally distributed population with unknown s, an alternative method (not used in this book) is to use the methods of this section if the sample is small (n # 30), but if the sample is large
32. Appendix B Data Set: Tobacco Use in Children’s Movies Refer to Data Set 5 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
31. Appendix B Data Set: Pulse Rates The author, at the peak of an exercise program, claimed that his pulse rate was lower than the mean pulse rate of a typical male. The author’s pulse rate was measured to be 60 beats per minute. Use the pulse rates of the males listed in Data Set 1 in Appendix
30. Appendix B Data Set: Forecast Errors Refer to Data Set 8 in Appendix B and subtract each actual high temperature from the high temperature that was forecast one day before. The result is a list of errors. Test the claim that all such errors have a mean equal to 0. What does the result suggest
29. Appendix B Data Set: Weights of Quarters Use the weights of the post-1964 quarters listed in Data Set 14 from Appendix B. Test the claim that the quarters are manufactured according to the U.S. mint specification that the mean is equal to 5.670 g.
28. 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
27. World’s Smallest Mammal The world’s smallest mammal is the bumblebee bat, also known as the Kitti’s hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these bats. Test the claim that
26. Sugar in Cereal Different cereals are randomly selected, and the sugar content(grams of sugar per gram of cereal) is obtained for each cereal, with the results given below for Cheerios, Harmony, Smart Start, Cocoa Puffs, Lucky Charms, Corn Flakes, Fruit Loops, Wheaties, Cap’n Crunch, Frosted
25. Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter, or in the air. The Environmental Protection Agency has established an air quality standard for lead of The measurements shown below were recorded at Building 5 of the World Trade Center site on
24. 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
23. Heights of Supermodels The heights are measured for supermodels Niki Taylor, Nadia Avermann, Claudia Schiffer, Elle MacPherson, Christy Turlington, Bridget Hall, Kate Moss, Valeria Mazza, and Kristy Hume. They have a mean of 70.2 in.and a standard deviation of 1.5 in. Use a 0.01 significance
22. Effectiveness of Diet Forty subjects followed the Weight Watchers diet for a year.Their weight changes are summarized by these statistics: s 5 10.8 lb(based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone x 5 26.6 lb, x 5 4.00, x 5 660.3, x 5 2700 g, SPSS 434 Chapter
21. Treating Chronic Fatigue Syndrome Patients with chronic fatigue syndrome were tested, then retested after being treated with fludrocortisone. A standard scale from 27 to 17 is used to measure fatigue before and after the treatment. The changes are summarized with these statistics: n 5 21, s 5
20. Credit Rating When consumers apply for credit, their credit is rated using FICO(Fair, Isaac, and Company) scores. A random sample of credit ratings is obtained, and the FICO scores are summarized with these statistics: n 5 18, s 5 95.9.Use a 0.05 significance level to test the claim that these
19. Birth Weights In a study of the effects of prenatal cocaine use on infants, the following sample data were obtained for weights at birth: n 5 190, s 5 645 g(based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer, et al., Journal of the
18. 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
17. Body Temperatures Data Set 2 in Appendix B includes 106 body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F. Use a 0.05 significance level to test the claim that the mean body temperature is less than 98.6°F. Based on these results, does it appear that the commonly
4. Reality Check Unlike the preceding section, this section does not include a requirement that the value of the population standard deviation must be known. Which section is more likely to apply in realistic situations: this section or the preceding section? Why?
3. Unnecessary Test A quality control manager claims that cans of cola are being filled with amounts having a mean that is less than 12 oz. If the sample data consist of 24 cans with a mean of 12.13 oz and a standard deviaton of 0.12 oz, why is it not necessary to conduct a formal hypothesis test
2. Normal and t Distributions Identify two characteristics that the standard normal and t distributions have in common, and identify two characteristics that are different for the normal and t distributions.
1. Degrees of Freedom When using Table A-3 to find critical values, we must use the appropriate number of degrees of freedom. If a sample consists of five values, what is the appropriate number of degrees of freedom? If you don’t know any of the five sample values, but you know that their mean is
21. Power of a Test The procedure for finding the power in a hypothesis test involving a proportion is given in Exercise 47 from Section 8-2. Use the same procedure to find the power of a hypothesis test of the claim that m . 100, given a sample of size 40, a known population standard deviation of
20. Appendix B Data Set: Forecast Errors Refer to Data Set 8 in Appendix B and subtract each actual high temperature from the high temperature that was forecast one day before.The result is a list of errors. Assuming that all such errors have a standard deviation of 2.5°, use a 0.05 significance
19. Appendix B Data Set: Weights of Quarters Use the weights of the post-1964 quarters listed in Data Set 14 from Appendix B. Assuming that quarters are minted to produce weights with a population standard deviation of 0.068 g, use the sample of weights with a 0.01 significance level to test the
18. World’s Smallest Mammal The world’s smallest mammal is the bumblebee bat, also known as the Kitti’s hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these bats. Assuming that the
17. Blood Pressure Levels When 14 different second-year medical students at Bellevue Hospital measured the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 10 mmHg, use a 0.05 significance
16. Are Thinner Aluminum Cans Weaker? An axial load of an aluminum can is the maximum weight that the sides can support before collapsing. The axial load is an important measure, because the top lids are pressed onto the sides with pressures that vary>>> >Excel (DDXL) Display for Exercise 11
15. Does the Diet Work? When 40 people used the Atkins diet for one year, their mean weight change was 22.1 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger, et al., Journal of the American
14. 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.
13. Perception of Time Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 min (or 60 sec) has passed.Forty students yielded a sample mean of 58.3 sec. Assuming that s 5 9.5 sec, use a 0.05 significance level to test the claim
12. 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 ng ml. Assuming that s is known to be 119.5 ng ml, test the claim that the mean cotinine level of all smokers is
11. Everglades Temperatures In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.377°C is obtained for 61 temperatures recorded on 61
10. Human Body Temperature Data Set 2 in Appendix B includes a sample of 106 body temperatures with a mean of 98.20°F. Assume that s is known to be 0.62°F. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean body temperature of the population is less
9. M&Ms Data Set 13 in Appendix B includes a sample of 27 blue M&Ms with a mean weight of 0.8560 g. Assume that s is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean weight of all M&Ms is equal to 0.8535 g (the weight necessary so
4. Systematic Sampling A dean obtains a sample at a college by selecting every 50th name in the list of all 6000 current full-time students. She then proceeds to test the claim that the mean grade-point average is greater than 2.50. Is the sample a simple random sample? Is the sample likely to be
3. Confidence Interval You want to test the claim that m , 100 by constructing a confidence interval. If the hypothesis test is to be conducted with a 0.01 significance level, what confidence level should be used for the confidence interval?
2. Verifying Requirements A simple random sample consists of n 5 12 values, so the requirement of normality must be checked. How can you check that requirement of normality?
If the sample results (or more extreme results) can easily occur when the assumption (null hypothesis) is true, we attribute the relatively small discrepancy between the assumption and the sample results to chance.● If the sample results (or more extreme results) cannot easily occur when the
1. Requirements Must you have a sample size of n . 30 in order to use the methods of hypothesis testing presented in this section? If a simple random sample has fewer than 31 values, what requirement must be satisfied to justify using the methods of this section?interval method is somewhat
33. Power 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.a. Using an alternative hypothesis of p , 0.4, a
32. 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
31. 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
30. Using the Continuity Correction Repeat Exercise 28, but include the correction for continuity that was described in Section 6-6. How are the results affected by including the continuity correction?
29. 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
28. Alcohol and Tobacco Use in Animated Children’s Movies Using results listed in Data Set 5 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.8-3 BEYOND THE BASICS
27. Accuracy of Forecast Temperatures Refer to Data Set 8 in Appendix B. Find the proportion of days with an actual high temperature that is more than 2° different from the high temperature that was forecast one day before. Let p represent the proportion of days with an actual high temperature
26. Precipitation in Boston Refer to Data Set 10 in Appendix B, and note that days with any precipitation have values different from 0. Use a 0.05 significance level to test the claim that on Sundays in Boston, there is precipitation more than 25% of the days.
25. Using M&M Data Refer to Data Set 13 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 24% of its plain M&M candies are blue.
24. Smoking and College Education One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke and 81.7% 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
23. Testing Clarinex for Adverse Reaction Clarinex is a drug used to treat asthma. In clinical tests of this drug, 1655 patients were treated with 5-mg doses of Clarinex, and 2.1% of them experienced fatigue (based on data from the Schering Corporation). Use a 0.01 significance level to test the
22. Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Mexican-Americans. Among the people eligible for grand jury duty, 79.1% were Mexican-Americans.
21. Flying In a Gallup poll of 1125 adults, it was found that 47% fly never or rarely. Use a 0.05 significance level to test the claim that the percentage of adults who fly never or rarely is equal to 50%. Given that the survey subjects volunteered an answer to a question about flying, is it
20. Smoking In a Gallup poll of 1018 adults, it was found that 22% smoked cigarettes in the past week. Use a 0.05 significance level to test the claim that less than 25% of adults have smoked within the past week. Would the conclusion change if, instead of a Gallup poll, the results were obtained
19. Drinking Survey A recent Gallup poll of 976 randomly selected adults showed that 312 of them never drink. Use those survey results to test the claim that less than 1 3 of all adults never drink. Use a 0.05 significance level. Also, examine the following wording of the actual question and
18. Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone their death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, it was found that there were 6062 deaths in the week before Thanksgiving, and there
17. Store Checkout Scanner Accuracy In a study of store checkout scanners, 1234 items were checked and 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from “UPC Scanner Pricing Systems: Are They Accurate?” by Goodstein, Journal of
16. 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 “High-Dose Nicotine Patch Therapy,” by Dale et al.,
15. 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 Minitab Display for Exercise 8 416 Chapter 8
14. 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
13. 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.
12. Travel Through the Internet Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for making travel
11. Car Crashes In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home (based on data from Progressive Insurance). Use a 0.01 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home. Are the results questionable
10. Gender Selection for Boys The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As this book was being written, 51 babies were born to parents using the YSORT method, and 39 of them were boys. Use the sample data
9. Gender Selection for Girls The Genetics and IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As this book was being written, 325 babies were born to parents using the XSORT method, and 295 of them were girls. Use the sample
8. Percentage of Telephone Users Asurvey of 4276 randomly selected households showed that 4019 of them had telephones (based on data from the U.S. Census Bureau). Minitab was used to test the claim that the percentage of households is now greater than the 35%rate that was found in 1920. The Minitab
7. Interpreting Display When 109,857 arrests for federal offenses were randomly selected, it was found that 31,969 of them were drug offenses. When testing the claim that more than 29% of federal crimes were for drug offenses, the accompanying TI-83 84 Plus calculator display was obtained. Use the
6. Survey of Workers In a survey of 703 randomly selected workers, 15.93% got their jobs through newspaper ads (based on data from Taylor Nelson Sofres Intereach).Consider a hypothesis test that uses a 0.05 significance level to test the claim that less than 20% of workers get their jobs through
5. 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
4. P-Value Method A P-value of 0.00001 is obtained when using sample data to test the claim that the majority of car crashes occur within 5 miles of home. Interpret this P-value in the context of this hypothesis test. That is, what does the P-value tell us?In Exercises 5–8, identify the indicated
3. Sampling America Online conducts a survey in which Internet users are asked to respond to a question. Among the 96,772 responses, there are 76,885 responses of“yes.” Is it valid to use these sample results for testing the claim that the majority of the general population answers “yes”?
2. Sample Proportion When respondents are asked a question on a survey, 40 of them answer yes, 60 of them answer no, and there are no other responses. What is the sample proportion of yes responses, and what notation is used to represent it?
1. Distribution Assuming that the listed requirements of this section are satisfied, what distribution is used to test a claim about a population proportion? Why?
48. Finding Sample Size Aresearcher plans to conduct a hypothesis test using the alternative hypothesis of H1: p , 0.4, and she plans to use a significance level of a 5 0.05.Find the sample size required to achieve at least 80% power in detecting a reduction in p from 0.4 to 0.3. (This is a very
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 64.a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when
11. Out-of-class activity Each student should find an article in a professional journal that includes a confidence interval of the type discussed in this chapter. Write a brief report describing the confidence interval and its role in the context of the article.
10. Out-of-class activity Identify a topic of general interest and coordinate with all members of the class to conduct a survey. Instead of conducting a “scientific” survey using sound principles of random selection, use a convenience sample consisting of respondents that are readily available,
9. In-class activity Divide into groups of two. First find the sample size required to estimate the proportion of times that a coin turns up heads when tossed, assuming that you want 80% confidence that the sample proportion is within 0.08 of the true population proportion.Then toss a coin the
8. In-class activity Divide into groups of three or four. Examine a current magazine such as Time or Newsweek, and find the proportion of pages that include advertising.Based on the results, construct a 95% confidence interval estimate of the percentage of all such pages that have advertising.
7. In-class activity Each student should estimate the length of the classroom. The values should be based on visual estimates, with no actual measurements being taken. After the estimates have been collected, construct a confidence interval, then measure the length of the room. Does the confidence
6. In-class activity A class project should be designed to conduct a test in which each student is given a taste of Coke and a taste of Pepsi. The student is then asked to identify which sample is Coke. After all of the results are collected, analyze the claim that the success rate is better than
5. In-class activity Each student should write an estimate of the age of the current President of the United States.All estimates should be collected and the sample mean and standard deviation should be calculated. Then use the sample results to construct a confidence interval.Do the confidence
4. Out-of-class activity Groups of three or four students should go to the library and collect a sample consisting of the ages of books (based on copyright dates). Plan and describe the sampling plan, execute the sampling procedure, then use the results to construct a confidence interval estimate
3. In-class activity Assume that a method of gender selection can affect the probability of a baby being a girl, so that the probability becomes Each student should simulate 20 births by drawing 20 cards from a shuffled deck. Replace each card after it has been drawn, then reshuffle. Consider the
2. In-class activity Without using any measuring device, each student should draw a line believed to be 3 in.long and another line that is 3 cm long. Then use rulers to measure and record the lengths of the lines drawn. Find the means and standard deviations of the two sets of lengths. Use the
1. Out-of-class activity Collect sample data, and use the methods of this chapter to construct confidence interval estimates of population parameters. Here are some suggestions for parameters:● Proportion of students at your college who can raise one eyebrow without raising the other eyebrow.
3. 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 includes 111 people who took trips that included visits to theme parks, and there were 1122 other respondents who took trips
2. X-Linked Recessive Disorders A genetics expert has determined that for certain couples, there is a 0.25 probability that any child will have an X-linked recessive disorder.a. Find the probability that among 200 such children, at least 65 have the X-linked recessive disorder.b. A subsequent study
1. Analyzing Weights of Supermodels Supermodels are sometimes criticized on the grounds that their low weights encourage unhealthy eating habits among young women.Listed below are the weights (in pounds) of nine randomly selected supermodels.125 (Taylor) 119 (Auermann) 128 (Schiffer) 128
8. 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
7. Smoking and College Education The tobacco industry closely monitors all surveys that involve smoking. One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke (based on data from the American Medical Association).a. Construct the 98% confidence

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