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statistics informed decisions using data
Elementary Statistics 10th Edition Mario F. Triola - Solutions
11. Home Field Advantage When games were sampled from throughout a season, it was found that the home team won 127 of 198 professional basketball games, and the home team won 57 of 99 professional football games (based on data from “Predicting Professional Sports Game Outcomes from Intermediate
8. From a CNN>USAToday>Gallup poll: Among 1003 survey subjects, 11% say that the opinion of a celebrity would influence their own opinion.Calculations for Testing Claims. In Exercises 9 and 10, assume that you plan to use a significance level of a 0.05 to test the claim that p1 p2. Use the
7. From a Gallup poll: Among 976 survey subjects, 7% have an alcoholic drink every day.
6. From a Gallup poll: Among 1018 survey subjects, 22% smoked cigarettes in the past week.
5. From a New York Times article: Among 3250 pedestrian walk buttons in New York City, 23% of them work.
4. Equivalence of Hypothesis Tests and Confidence Intervals Given sample proportions from two different populations, we want to use a 0.05 significance level to test the claim that p1 p2. One approach is to use the P-value method of hypothesis testing, a pˆ, p, p pˆ, p, p z 5 spˆ1 2 pˆ2d 2
3. Interpreting Confidence Interval Sample data from two different populations are used to construct this 95% confidence interval: 0.200 p1 – p2 0.300. Write a statement interpreting that confidence interval.
2. What do the symbols represent?
1. Pooled Sample Proportion What is a pooled sample proportion and what is the symbol that represents it? Is it used for hypothesis tests and confidence intervals?
d. Assuming that the dogs did better than what would be expected with random guessing, did they do well enough to be used for actual medical diagnoses? Why or why not?
c. Among the 54 trials, there were 22 correct identifications. Test the hypothesis that the dogs did significantly better than what would be expected with random guessing. Does it appear that the dogs were guessing, or do they appear to have some ability to identify the cancer sample?
b. Given that the trial was conducted 54 times, what is the expected number of correct identifications, assuming that random guesses were made?
a. Given that each trial involved six healthy samples and one sample from a patient with bladder cancer, what is the probability that a dog would select the cancer sample if it made a random guess?
What is the probability of economic rise in
3. SAT Math Scores of Women The math SAT scores for women are normally distributed with a mean of 496 and a standard deviation of 108.a. If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 500.b. If five math SAT scores are randomly
2. Normal Quantile Plot Refer to the data listed in Exercise 1 and construct a normal quantile plot. Based on the result, do the heights appear to come from a population that is normally distributed?
1. Heights of Presidents Listed below are the heights (in inches) of the Presidents who served in the 20th century. Assume that these values are sample data from some larger population.67 70 72 71 72 70 71 74 69 70.5 72 75 71.5 69.5 73 74 74.5a. Find the mean.b. Find the median.c. Find the standard
12. Nicotine in Cigarettes The Carolina Tobacco Company advertised that its best-selling 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
11. 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
10. Heights of Women Anthropometric survey data are used to publish values that can be used in designing products that are suitable for use by adults. According to Gordon, Churchill, et al., women have heights with a mean of 64.1 in. and a standard deviation of 2.52 in. The sample of 40 heights of
9. Body Temperature Apremed student in a statistics class is required to do a class project.Intrigued by the body temperatures in Data Set 2 of Appendix B, she plans to collect her own sample data to test the claim that the mean body temperature is less than 98.6°F, as is commonly believed.
8. Random Generation of Data The TI-83 84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(100,15,50)generates 50 values from a normally distributed population with m 5 100 and s 5 15.One such generated sample of 50 values has a mean
7. IQ Scores For a simple random sample of adults, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Asimple random sample of 13 statistics professors yields a standard deviation of s 5 7.2. A psychologist is quite sure that statistics professors have IQ scores
6. Testing Lipitor for Adverse Effects 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 claim
5. Are Consumers Being Cheated? The Orange County Bureau of Weights and Measures received complaints that the Windsor Bottling Company was cheating consumers by putting less than 12 oz of root beer in its cans. When 24 cans are randomly selected and measured, the amounts are found to have a mean of
4. Weights of Sugar Packets A student of the author randomly selected 70 packets of sugar and weighed the contents of each packet, getting a mean of 3.586 g and a standard deviation of 0.074 g. Test the claim that the weights of the sugar packets have a mean equal to 3.5 g, as indicated on the
3. 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
2. Interviewing Mistakes An Accountemps survey of 150 executives showed that 44%of them say that “little or no knowledge of the company” is the most common mistake made by candidates during job interviews (based on data from USA Today). Use a 0.05 significance level to test the claim that less
1. Identifying Hypotheses, Distributions, and Verifying Requirements Based on the given conditions, identify the alternative hypothesis. Also, either identify the sampling distribution(normal, t, chi-square) of the test statistic, or state that the methods of this chapter should not be used.Table
2. Sample You have just collected a very large (n 5 2575) sample of responses obtained from adult Americans who mailed responses to a questionnaire printed in Fortune magazine. If this sample is used to make inferences about a population, what is the population? A hypothesis test conducted at the
1. Practical Significance When testing the claim that the mean amount lost on a diet is greater than 0 lb, we use sample results showing that 10,000 people lost amounts with a mean of 0.1 lb. Also, the sample standard deviation is 0.8 lb. The hypothesis test results include a test statistic of t 5
20. Appendix B Data for Precipitation Amounts Refer to Data Set 8 in Appendix B and use the sample data consisting of the precipitation amounts. Test the claim that these amounts are from a population with a standard deviation less than 1.00 in. Use a significance level of 0.05. Does the
19. Appendix B Data for Weights of Quarters Refer to Data Set 14 in Appendix B and use the sample data consisting of weights of quarters made after 1964. Test the claim that these quarters come from a population with a standard deviation equal to the specified value of 0.068 g. Use a significance
17. 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
16. Supermodel Heights Use a 0.05 significance level to test the claim that heights of female supermodels vary less than the heights of women in general. The standard deviation of heights of the population of women is 2.5 in. Listed below are the 8-6 Testing a Claim About a Standard Deviation or
14. 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. Using a 0.05
13. Credit Rating When consumers apply for credit, their credit is rated using FICO(Fair, Isaac, and Company) scores. Credit ratings are given below for a sample of applicants for car loans, and these applicants are all from a new branch of the Bank of Newport. Use the sample data to test the claim
12. Manufacturing Aircraft Altimeters The Stewart Aviation Products Company uses a new production method to manufacture aircraft altimeters. A simple random sample of 81 altimeters is tested in a pressure chamber, and the errors in altitude are recorded as positive values (for readings that are too
11. Variation in Peanut M&Ms Use a 0.01 significance level to test the claim that peanut M&M candies have weights that vary more than the weights of plain M&M candies.The standard deviation for the weights of plain M&M candies is 0.056 g. A sample of 41 peanut M&Ms has weights with a standard
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.
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