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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

5. Claim: The treatment population and the placebo population have different variances.Treatment group: n 16, 21.33, s 0.80 Placebo group: n 41, 25.34, s 0.40
4. F Distribution Identify two different properties of the F distribution.Hypothesis Test of Equal Variances. In Exercises 5 and 6, test the given claim. Use a significance level of a 0.05 and
3. F Distribution In the context of this section, what is the F distribution?
2. Effects of Nonnormal Distributions What is a consequence of using the F test with samples from populations with distributions that are not normal? That is, in what way does the test perform poorly?
1. Weakness of F Test What is a major weakness of the F test described in this section?Name two alternatives that do a better job of overcoming that weakness.
27. Using the Correct Procedurea. Consider the sample data given below to be matched pairs and use a 0.05 significance level to test the claim that md 0.b. Consider the sample data given below to
26. Effects of an Outlier and Units of Measurementa. When using the methods of this section, can an outlier have a dramatic effect on the hypothesis test and confidence interval?9-5 Comparing
25. SAT Training Course The article “An SAT Coaching Program That Works” (by Kaplan, Chance, Vol. 15, No. 1) included a graph similar to the one shown below. The points represent the SAT scores
24. Appendix B Data Set: Old Faithful Refer to Data Set 11 in Appendix B and use the time intervals before and after each eruption.a. Using a 0.05 significance level, test the claim that the
23. Appendix B Data Set: Home Prices Refer to Data Set 18 in Appendix B and use the selling prices and list prices of homes sold.a. Using a 0.05 significance level, test the claim of a realtor that
22. Appendix B Data Set: Tobacco and Alcohol in Children’s Movies Refer to Data Set 5 in Appendix B. Use the paired data consisting of times that the movies showed tobacco use and the times that
21. Appendix B Data Set: Forecast Temperatures The examples in this section used only five pairs of sample data so that the calculations would be easy. Refer to Data Set 8 in Appendix B and use all
20. Confidence Interval for Comparing Keyboards The traditional keyboard configuration is referred to as a QWERTY configuration because of the positions of the letters QWERTY on the top row of keys.
19. Testing Corn Seeds In 1908, William Gosset published the article “The Probable Error of a Mean” under the pseudonym of “Student” (Biometrika, Vol. 6, No. 1). He included the data listed
18. Measuring Intelligence in Children Mental measurements of young children are often made by giving them blocks and telling them to build a tower as tall as possible.One experiment of block
17. Effectiveness of Hypnotism in Reducing Pain A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the
16. Self-Reported and Measured Male Heights As part of the National Health and Nutrition Examination Survey conducted by the Department of Health and Human Services, self-reported heights and
15. SAT Training Course The article “An SAT Coaching Program That Works,” by Kaplan (Chance, Vol. 15, No. 1) included a graph depicting SAT scores for 50 subjects in a control group. Nine of the
14. Heights of Winners and Runners-Up Listed below are the heights of candidates who won presidential elections and the heights of the candidates with the next highest number of popular votes. The
13. Measuring Blood Pressure Fourteen different medical students measured the blood pressure of the same patient, then repeated the measurement the following day. Listed below are the systolic
12. Is Friday the 13th Unlucky? Researchers collected data on the numbers of hospital admissions resulting from motor vehicle crashes, and results are given below for Fridays on the 6th of a month
b. Construct a 95% confidence interval estimate of the mean difference between actual high temperatures and high temperatures forecast one day earlier. Interpret the resulting confidence interval,
11. Forecast Temperatures Examples in this section included actual low temperatures and low temperatures that were forecast five days earlier. Listed below are actual high temperatures and the high
10. Interpreting Display for Test with Before After Treatment Results Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood
9. Interpreting Display of Test for Treating Motion Sickness The following Minitab display resulted from an experiment in which 10 subjects were tested for motion sickness before and after taking the
8. Confidence Interval Using the sample paired data in Exercise 6, construct a 99%confidence interval for the population mean of all differences x y.
7. Confidence Interval Using the sample paired data in Exercise 5, construct a 95%confidence interval for the population mean of all differences x y.
4. Boxplots The examples in this section are based on matched actual forecast temperature data. For those examples, would it make sense to construct a boxplot of the actual temperatures and another
3. Notation What do the symbols and sd denote?
2. Matching with Coin Tosses A researcher is investigating measures of intelligence and obtains IQ scores of 24 subjects configured as 12 matched pairs, with the matching based on coin tosses. Can
1. Bear Heights and Weights Sample data consist of heights and weights of 12 randomly selected bears. When analyzing the relationship between height and weight, do the methods of this section apply?
37. Calculating Degrees of Freedom How is the number of degrees of freedom for Exercises 19 and 20 affected if Formula 9-1 is used instead of selecting the smaller of n1 – 1 and n2 – 1? If
36. Effect of No Variation in Sample An experiment was conducted to test the effects of alcohol. The breath alcohol levels were measured for a treatment group of people who drank ethanol and another
35. Verifying a Property of Variancesa. Find the variance for this population of x values: 5, 10, 15. (See Section 3-3 for the variance of a population.)b. Find the variance for this population of y
34. Effects of Units of Measurement How are the results of Exercise 24 affected if all of the ages are converted from years to months? In general, does the choice of the scale affect the conclusions
33. Effects of an Outlier Refer to Exercise 24 and include an outlier consisting of a car that is 50 years old. Is the hypothesis test dramatically affected by the presence of the outlier?
32. Confidence Interval with Pooling Do Exercise 18 with the additional assumption that. How are the results affected by this additional assumption?
31. Hypothesis Test with Pooling Do Exercise 17 with the additional assumption that. How are the results affected by this additional assumption?
30. Hypothesis Test with Pooling Do Exercise 13 with the additional assumption that. How are the results affected by this additional assumption?
29. Confidence Interval with Pooling Do Exercise 12 with the additional assumption that. How are the results affected by this additional assumption?
28. Appendix B Data Set: Weights of Coke Refer to Data Set 12 in Appendix B and test the claim that because they contain the same amount of cola, the weights of cans of regular Coke have the same
27. Appendix B Data Set: Weights of Quarters Weights of quarters are used by vending machines as one way to detect counterfeit coins. Refer to Data Set 14 in Appendix B and test the claim that the
26. Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for
25. Tar and Cigarettes Refer to the sample data listed below and use a 0.05 significance level to test the claim that the mean amount of tar in filtered king-size cigarettes is less than the mean
24. Hypothesis Test for Difference in Car>Taxi Ages When the author visited Dublin in Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded
23. Hypothesis Test for Difference in Home Values Listed below are fair market values(in thousands of dollars) of randomly selected homes on Long Beach Island in New Jersey. Use a 0.05 significance
22. Hypothesis Test for Effects of Alcohol Refer to the sample data in Exercise 21 and use a 0.05 significance level to test the claim that there is a difference between the treatment group and
21. Confidence Interval for Effects of Alcohol An experiment was conducted to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of
20. Hypothesis Test for Identifying Psychiatric Disorders Refer to the sample data in Exercise 19 and use a 0.01 significance level to test the claim that there is a difference between the two
19. Confidence Interval for Identifying Psychiatric Disorders Are severe psychiatric disorders related to biological factors that can be physically observed? One study used x-ray computed tomography
18. Confidence Interval for Magnet Treatment of Pain Refer to the sample data from Exercise 17 and construct a 90% confidence interval estimate of the difference between the mean reduction in pain
17. Hypothesis Test for Magnet Treatment of Pain People spend huge sums of money(currently around $5 billion annually) for the purchase of magnets used to treat a wide xx xx 9-3 Inferences About Two
16. Hypothesis Test for Bipolar Depression Treatment Refer to the sample data in Exercise 15 and use a 0.05 significance level to test the claim that the treatment group and placebo group come from
15. Confidence Interval for Bipolar Depression Treatment In clinical experiments involving different groups of independent samples, it is important that the groups be similar in the important ways
14. Confidence Interval for Effects of Marijuana Use on College Students Refer to the sample data used in Exercise 13 and construct a 98% confidence interval for the difference between the two
13. Hypothesis Test for Effect of Marijuana Use on College Students Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and
12. Confidence Interval for Comparing Diets Arandomized trial tested the effectiveness of diets on adults. Among 40 subjects using the Weight Watchers diet, the mean weight loss after one year was
11. Confidence Interval for Effect of Birth Weight on IQ Score When investigating a relationship between birth weight and IQ, researchers found that 258 subjects with extremely low birth weights
10. Hypothesis Test of Effects of Cocaine on Children A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for
9. Hypothesis Test of Effectiveness of Echinacea In a randomized, double-blind, placebo-controlled trial of children, echinacea was tested as a treatment for upper respiratory infections in children.
8. The effectiveness of a flu vaccine is tested by treating one group of subjects with the vaccine while another group of subjects is given placebos.In Exercises 9–28, assume that the two samples
7. The effectiveness of the Weight Watchers diet is tested in an experiment, and for each subject, the weight before the diet and the weight after the diet are recorded.
6. The effectiveness of Prilosec for treating heartburn is tested by measuring gastric acid secretion in patients before and after the drug treatment. The data consist of the before after
5. The effectiveness of Prilosec for treating heartburn is tested by measuring gastric acid secretion in a group of patients treated with Prilosec and another group of patients given a placebo.
. Before After Data A random sample of subjects is treated with a drug intended to lower their cholesterol levels. For each subject, the cholesterol is measured once before the treatment and once
3. Degrees of Freedom In the hypothesis test example in this section, the critical value of t 1.717 was obtained by using df smaller of n1 – 1 and n2 – 1. With sample sizes of 23 and 30, we
2. Confidence Interval for Hypothesis Testing You plan to construct a confidence interval to be used for testing the claim that one population has a mean greater than the other. If the test is to
1. Requirements See the age data used in the hypothesis testing and confidence interval examples of this section. If we include one more age of 80 years for an unsuccessful applicant, are the
c. Use the preceding results to verify that the variance of the difference between two independent random variables is the sum of their individual variances.
b. Assuming that two quarters are tossed, the sample space and variance will be the same as in part (a). List the 16 differences in proportions that are possible when every outcome of the two dimes
a. Assuming that two dimes are tossed, list the sample space of four simple events, then find the proportion of heads in each of the four cases. Use the formula to find the variance for the
37. Verifying Property of Variances When discussing the rationale for the methods of this section, it was stated that because and are each approximated by a normal distribution, will also be
36. Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 can be found as follows.
35. Testing for Constant Difference To test the null hypothesis that the difference between two population proportions is equal to a nonzero constantc, use the test statistic As long as n1 and n2 are
34. Equivalence of Hypothesis Test and Confidence Interval Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common
d. Based on the preceding results, what should you conclude about equality of p1 and p2? Which of the three preceding methods is least effective in testing for equality of p1 and p2?
c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?
b. Use the methods of Section 7-2 to construct individual 95% confidence interval estimates for each of the two population proportions. After comparing the overlap between the two confidence
33. Interpreting Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman
32. Appendix B Data Set: Health Survey Refer to Data Set 1 in Appendix B and use the sample data to test the claim that the proportion of men over the age of 30 is equal to the proportion of women
31. Appendix B Data Set: Alcohol and Tobacco in Children’s Movies Test the claim that the proportion of 25 of 50 randomly selected children’s movies showing some use of alcohol is significantly
30. Appendix B Data Set: Precipitation Data Set 8 in Appendix B lists precipitation amounts for the author’s home in Dutchess County, New York. Data Set 10 in Appendix B lists precipitation amounts
29. Appendix B Data Set: Precipitation Data Set 10 in Appendix B lists precipitation amounts for Boston. Consider a day to have precipitation if the amount is any positive value. Test the claim that
28. Attitudes Toward Marriage Refer to the same sample data as in the preceding exercise and use a 0.01 significance level to test the claim that there is a difference between the proportion of men
27. Attitudes Toward Marriage In a Time CNN survey, 24% of 205 single women said that they “definitely want to get married.” In the same survey, 27% of 260 single men gave that same response.
26. Incidence of Radon Radon is a gas produced when radium decays, and it can enter homes where it can become a health threat. Among 186 homes in Hyde Park, New York (home of Franklin D. Roosevelt),
25. Gender Gap for Seat Belt Use? Among 2200 randomly selected male car occupants over the age of 8, 72% wear seat belts. Among 2380 randomly selected female car occupants over the age of 8, 84% wear
24. Lost Baggage Among 5000 items of randomly selected baggage handled by American Airlines, 22 were lost. Among 4000 items of randomly selected baggage handled by Delta Airlines, 15 were lost (based
23. Driving to Work In a survey of commuting habits, it was found that among 1068 homeowners, 82.4% drive themselves to work. Among 1064 renters, 68.1% drive themselves to work (based on data from
22. Adverse Effects of Clarinex Use the same sample data as in the preceding exercise. If you plan to test the given claim by constructing a confidence interval, what confidence level should be used?
21. Adverse Effects of Clarinex The drug Clarinex is used to treat symptoms from allergies.In a clinical trial of this drug, 2.1% of the 1655 treated subjects experienced fatigue.Among the 1652
20. Testing Effectiveness of Vaccine In a USA Today article about an experimental nasal spray vaccine for children, the following statement was presented: “In a trial involving 1602 children only
19. Effectiveness of Smoking Bans The Joint Commission on Accreditation of Healthcare Organizations mandated that hospitals ban smoking by 1994. In a study of the effects of this ban, subjects who
18. E-mail and Privacy Refer to the sample data given in Exercise 17 and construct a 90% confidence interval estimate of the difference between the two population proportions.Is there a substantial
17. E-mail and Privacy Asurvey of 436 workers showed that 192 of them said that it was seriously unethical to monitor employee e-mail. When 121 senior-level bosses were surveyed, 40 said that it was
16. Telephone Survey Methods The preceding exercise involves a one-sided hypothesis test with a 0.01 significance level. If you plan to test the claim using a confidence interval, what confidence
15. Telephone Survey Methods In a study of the accuracy of telephone surveys, 720 people refused to respond when they were among the 1720 people included in a “standard”5-day survey. In the same
14. Do Bednets Reduce Malaria? In a randomized controlled trial in Kenya, insecticidetreated bednets were tested as a way to reduce malaria. Among 343 infants who used the bednets, 15 developed
13. Gender Selection The Genetics and IVF Institute conducted a clinical trial of its methods for gender selection. As this book was written, results included 325 babies born to parents using the
12. Testing Laboratory Gloves The New York Times ran an article about a study in which Professor Denise Korniewicz and other Johns Hopkins researchers subjected laboratory gloves to stress. Among 240

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