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biostatistics
Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions
Cell Phone Radiation Here is a sample of measured radiation emissions (cW>kg) for cell phones (based on data from the Environmental Working Group): 38, 55, 86, 145.Here are ten bootstrap samples: {38, 145, 55, 86}, {86, 38, 145, 145}, {145, 86, 55, 55}, {55, 55, 55, 145}, {86, 86, 55, 55}, {38, 38,
Freshman 15 Repeat Exercise 7 “Freshman 15” using a confidence level of 90% for parts(a) and (b) and using 1000 bootstrap samples instead of the 10 that were given in Exercise 7.
Cell Phone Radiation Repeat Exercise 8 “Cell Phone Radiation” using a confidence level of 90% for parts (a) and (b), using 1000 bootstrap samples instead of the 10 that were given in Exercise 8.
ER Wait Times The District of Columbia has some of the longest emergency room waiting times in the United States. Here are times (minutes) patients waited in District of Columbia emergency rooms before seeing a physician: 40, 68, 72, 67, 54, 59, 68, 47, 55, 74, 63, 73.Use the bootstrap method with
ER Wait Times Repeat Exercise 11 “ER Wait Times” using these emergency room waiting times (minutes) from Florida: 29, 49, 31, 24, 14, 37, 43, 40, 35, 34, 10, 38, 2, 54.
Lipitor In clinical trials of the drug Lipitor (atorvastatin), 863 subjects were treated with 10 mg of the drug, and 8 of them experienced allergic reactions. Use the bootstrap method to construct a 95% confidence interval estimate of the percentage of treated subjects who experience allergic
Eliquis The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients.In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea (based on data from Bristol-Myers Squibb Co.). Use the bootstrap method to construct a 99%
Survey Return Rate In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online otological group(focused on ears), and 717 surveys were returned. Use the bootstrap method to construct a 90%confidence interval
Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use the bootstrap method to construct a 95% confidence interval estimate of the
Student Evaluations Listed below are student evaluation ratings of courses, where a rating of 5 is for “excellent.” The ratings were obtained at the University of Texas at Austin.Using the bootstrap method with 1000 bootstrap samples, construct a 90% confidence interval estimate of m. How does
Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands. Using the bootstrap method with 1000 bootstrap samples, construct a 99% confidence interval estimate of m. How does the result compare to the confidence interval
Cell Phone Radiation Here are the measured radiation emissions (in W>kg) from different cell phones: 0.38, 0.55, 1.54, 1.55, 0.50, 0.60, 0.92, 0.96, 1.00, 0.86, 1.46. Use the bootstrap method with 1000 bootstrap samples to find a 90% confidence interval estimate of m. How does the result compare to
Cell Phone Radiation Repeat Exercise 19 using the standard deviation instead of the mean.Compare the confidence interval to the one that would be found using the methods of Section 7-3.
Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below.5 0 1 0 2 0 5 0 5 0 3 8 5 0 5 0 5 6 0 0 0 0 0 0 8 5 5 0 4 5 0 0 4 0 0 0 0 0 8 0 9 5 3 0 5 0 0 0 5 8a. Use
Analysis of Last Digits Repeat Exercise 21 “Analysis of Last Digits” using the mean instead of the standard deviation. Compare the confidence interval to the one that would be found using the methods of Section 7-2.
Effect of the Number of Bootstrap Samples Repeat Exercise 21 “Analysis of Last Digits” using 10,000 bootstrap samples instead of 1000. What happens?
Distribution Shapes Use the sample data given in Exercise 21 “Analysis of Last Digits.”a. Do the original sample values appear to be from a normally distributed population? Explain.b. Do the 1000 bootstrap samples appear to have means that are from a normally distributed population? Explain.c.
Calculating Power Consider a hypothesis test of the claim that the Ericsson method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p 7 0.5. Assume that a significance level of a = 0.05 is used, and the sample is a simple random sample of
Exact Method For each of the three different methods of hypothesis testing (identified in the column at the left), enter the P-values corresponding to the given alternative hypothesis and sample data. Comment on the results. Normal approximation Exact Exact with simple continuity correction H: p =
Finding Critical Values of X2 For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value(s) found from technology or Table A-2. In Exercise 12 “Spoken Words,” we have df = 55, so Table A-4
Finding Critical Values of X2 Repeat Exercise 17 using this approximation (with k and z as described in Exercise 19): x = k(1 2 3 + 9k 9k
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 - a can be found by using the following expression:Replace n1 and n2 by n in the formula above (assuming that both samples have the
Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random
Yawning and Fisher’s Exact Test In one segment of the TV series Mythbusters, an experiment was conducted to test the common belief that people are more likely to yawn when they see others yawning. In one group, 34 subjects were exposed to yawning, and 10 of them yawned. In another group, 16
Ground vs. Helicopter for Serious Injuries A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from “Association
Lefties In a random sample of males, it was found that 23 write with their left hands and 217 do not. In a random sample of females, it was found that 65 write with their left hands and 455 do not (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education
Does Aspirin Prevent Heart Disease? In a trial designed to test the effectiveness of aspirin in preventing heart disease, 11,037 male physicians were treated with aspirin and 11,034 male physicians were given placebos. Among the subjects in the aspirin treatment group, 139 experienced myocardial
Headache Treatment In a study of treatments for very painful “cluster” headaches, 150 patients were treated with oxygen and 148 other patients were given a placebo consisting of ordinary air. Among the 150 patients in the oxygen treatment group, 116 were free from headaches 15 minutes after
Denomination Effect A trial was conducted with 75 women in China given a 100-yuan bill, while another 75 women in China were given 100 yuan in the form of smaller bills (a 50-yuan bill plus two 20-yuan bills plus two 5-yuan bills). Among those given the single bill, 60 spent some or all of the
Cell Phones and Handedness A study was conducted to investigate the association between cell phone use and hemispheric brain dominance. Among 216 subjects who prefer to use their left ear for cell phones, 166 were right-handed. Among 452 subjects who prefer to use their right ear for cell phones,
Bednets to Reduce Malaria In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria (based on data from“Sustainability of
Is Echinacea Effective for Colds? Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections(based on data from “An
Cardiac Arrest at Day and Night A study investigated survival rates for in-hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and
Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from “Who Wants Airbags?”by Meyer and Finney, Chance,
Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed
Dreaming in Black and White A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We
Are Radiation Effects the Same for Men and Women? Among 2739 female atom bomb survivors, 1397 developed thyroid diseases. Among 1352 male atom bomb survivors, 436 developed thyroid diseases (based on data from “Radiation Dose-Response Relationships for Thyroid Nodules and Autoimmune Thyroid
Smoking Cessation Programs Among 198 smokers who underwent a “sustained care”program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from“Sustained Care Intervention and
Clinical Trials of Lipitor Lipitor (atorvastatin) is a drug used to control cholesterol. In clinical trials of Lipitor, 94 subjects were treated with Lipitor and 270 subjects were given a placebo. Among those treated with Lipitor, 7 developed infections. Among those given a placebo, 27 developed
Ginkgo for Dementia The herb ginkgo biloba is commonly used as a treatment to prevent dementia. In a study of the effectiveness of this treatment, 1545 elderly subjects were given ginkgo and 1524 elderly subjects were given a placebo. Among those in the ginkgo treatment group, 246 later developed
Treating Carpal Tunnel Syndrome Carpal tunnel syndrome is a common wrist complaint resulting from a compressed nerve, and it is often the result of extended use of repetitive wrist movements, such as those associated with the use of a keyboard. In a randomized controlled trial, 73 patients were
Testing Laboratory Gloves The New York Times published an article about a study in which Professor Denise Korniewicz and other Johns Hopkins researchers subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses. Among 240 latex gloves, 7%leaked viruses. See the accompanying
Using Confidence Intervalsa. Assume that we want to use a 0.05 significance level to test the claim that p1 6 p2. Which is better: a hypothesis test or a confidence interval?b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent:
Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.a. Identify the null hypothesis and the alternative hypothesis.b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim?
Notation For the sample data given in Exercise 1, consider the Salk vaccine treatment group to be the first sample. Identify the values of n1, pn 1, qn 1, n2, pn 2, qn 2, p, and q. Round all values so that they have six significant digits.
Verifying Requirements In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo,
Odds Ratio In a study of the relationship between headaches and body weight, there were 4489 overweight subjects, and 331 of them experienced migraine headaches. Among 5487 subjects with normal weight, 358 experienced migraine headaches (based on data from “Body Mass Index and Episodic
Lightning Deaths Based on the results given in Cumulative Review Exercise 6, assume that for a randomly selected lightning death, there is a 0.8 probability that the victim is a male.a. Find the probability that three random people killed by lightning strikes are all males.b. Find the probability
Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 232 male deaths from lightning strikes and 55 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to construct a 95% confidence interval
Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 232 male deaths from lightning strikes and 55 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to test the claim that the proportion of
Lightning Deaths The accompanying bar chart shows the numbers of lightning strike deaths broken down by gender for a recent period of nine years. What is wrong with the graph?
Hypothesis Test for Lightning Deaths Refer to the sample data given in Cumulative Review Exercise 1 and consider those data to be a random sample of annual lightning deaths from recent years. Use those data with a 0.01 significance level to test the claim that the mean number of annual lightning
3. Confidence Interval for Lightning Deaths Use the sample values given in Cumulative Review Exercise 1 to construct a 99% confidence interval estimate of the population mean.Assume that the population has a normal distribution. Write a brief statement that interprets the confidence interval.
Lightning Deaths Refer to the sample data in Cumulative Review Exercise 1.a. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?b. Are the values discrete or continuous?c. Are the data categorical or quantitative?d. Is the sample a simple random sample?
Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of 14 recent and consecutive years. Find the values of the indicated statistics.51 44 51 43 32 38 48 45 27 34 29 26 28 23a. Meanb. Medianc. Standard deviationd. Variancee.
7. BMI for Miss America Use the same BMI indexes given in Exercise 6.Use a 0.01 significance level to test the claim that recent Miss America winners are from a population with a standard deviation equal to 1.34, which was the standard deviation of BMI for winners from the 1920s and 1930s. Do
BMI for Miss America A claimed trend of thinner Miss America winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for recent Miss America winners. Use a 0.01 significance level to test the claim that recent
Controlling Cholesterol The Westbrook Pharmaceutical Company manufactures atorvastatin pills, designed to lower cholesterol levels. Listed below are the amounts (in mg) of atorvastatin in a random sample of the pills. Use a 0.05 significance level to test the claim that the pills come from a
Smoking Recently, a simple random sample of 572 adult males showed that 124 of them smoke (based on data from the Centers for Disease Control and Prevention). It has been established that in 2008, 20.4% of adult males smoke. Use a 0.05 significance level to test the claim that the rate of smoking
Red Blood Cell Count A simple random sample of 40 adult males is obtained, and the red blood cell count (in cells per microliter) is measured for each of them, with these results:n = 40, x = 4.932 million cells per microliter, s = 0.504 million cells per microliter (from Data Set 1 “Body Data”
Is Nessie Real? This question was posted on the America Online website: Do you believe the Loch Ness monster exists? Among 21,346 responses, 64% were “yes.” Use a 0.01 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected
True , False Characterize each of the following statements as being true or false.a. In a hypothesis test, a very high P-value indicates strong support of the alternative hypothesis.b. The Student t distribution can be used to test a claim about a population mean whenever the sample data are
Equivalent Methods Which of the following statements are true?a. When testing a claim about a population mean m, the P-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.b. When testing a claim about a
Robust Explain what is meant by the statements that the t test for a claim about m is robust, but the x2 test for a claim about s2 is not robust.
Chi-Square Test In a test of the claim that s = 10 for the population of IQ scores of nurses, we find that the rightmost critical value is x2 R = 40.646. Is the leftmost critical x2 L value equal to -40.646?
Uncertainty True or false: If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true.
Conclusions True or false: The conclusion of “fail to reject the null hypothesis” has exactly the same meaning as “accept the null hypothesis.”
Conclusions True or false: In hypothesis testing, it is never valid to form a conclusion of supporting the null hypothesis.
P-Value Find the P-value in a test of the claim that the mean annual income of a nurse is greater than $60,000 (based on data from the Bureau of Labor Statistics) given that the test statistic is t = 2.462 for a sample of 30 nurses.
Instagram Poll In a Pew Research Center poll of Internet users aged 18−29, 53% said that they use Instagram. We want to use a 0.05 significance level to test the claim that the majority of Internet users aged 18−29 use Instagram.a. Identify the null and alternative hypotheses.b. Using a sample
Tails Determine whether the given claim involves a hypothesis test that is left-tailed, twotailed, or right-tailed.a. p 0.5b. m 6 98.6c. s 7 15
Distributions Using the methods of this chapter, identify the distribution that should be used for testing a claim about the given population parameter.a. Meanb. Proportionc. Standard deviation
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 significance
Queues Providence Hospital once had separate waiting lines for patients arriving for admission, but it now has a single waiting line that feeds the processing stations as vacancies occur. The standard deviation of waiting times with the old multiple-line configuration was 109.3 sec. Listed below is
Sphygmomanometers An aneroid sphygmomanometer is a mechanical device used to measure blood pressure. A random sample of these devices is tested for accuracy and the errors(mm Hg) are listed below (based on data from “How Accurate Are Sphygmomanometers?”by Mion and Pierin, Journal of Human
Weight Loss from Diet When 40 people used the Weight Watchers diet for one year, their weight losses had a standard deviation of 4.9 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.,
Spoken Words Couples were recruited for a study of how many words people speak in a day. A random sample of 56 males resulted in a mean of 16,576 words and a standard deviation of 7871 words. Use a 0.01 significance level to test the claim that males have a standard deviation that is greater than
New Filling Process The Orange Machine Company supplies a tool for pouring cold medicine into bottles in such a way that the standard deviation of the contents is 4.25 g. A new filling process is tested on 71 bottles and the standard deviation for this sample is 3.87 g. Use a 0.05 significance
Statistics Test Scores Tests in one of the author’s statistics classes have scores with a standard deviation equal to 14.1. One of his last classes had 27 test scores with a standard deviation of 9.3. Use a 0.01 significance level to test the claim that this class has less variation than other
Physician IQ Scores For a random sample of IQ scores of 18 physicians, the mean is 124.2 and the standard deviation is 9.6 (based on data from a study conducted at the University of Wisconsin at Madison). Use a 0.05 significance level to test the claim that because physicians are a more homogeneous
Birth Weights A simple random sample of birth weights of 30 girls has a standard deviation of 829.5 hg. Use a 0.01 significance level to test the claim that birth weights of girls have the same standard deviation as the birth weights of boys, which is 660.2 hg (based on Data Set 3 “Births” in
Body Temperature Example 5 in Section 8-3 involved a test of the claim that humans have body temperatures with a mean equal to 98.6 F. The sample of 106 body temperatures has a standard deviation of 0.62 F. The conclusion in that example would change if the sample standard deviation s were 2.08 F
Pulse Rates of Women Repeat the preceding exercise using the pulse rates of women listed in Data Set 1 “Body Data” in Appendix B. For the sample of pulse rates of women, n = 147 and s = 12.5. See the accompanying JMP display that results from using the original list of pulse rates instead of
Pulse Rates of Men A simple random sample of 153 men results in a standard deviation of 11.3 beats per minute (based on Data Set 1 “Body Data” in Appendix B). The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to
Birth Weights: Confidence Interval If we use the data given in Exercise 1, we get this 95% confidence interval estimate of the standard deviation of birth weights:0.486 kg 6 s 6 1.017 kg. When testing the claim that the sample is from a population with a standard deviation equal to 0.470 kg, what
Birth Weights For the sample data from Exercise 1, we get a P-value of 0.0291 when testing the claim that the sample is from a population with a standard deviation equal to 0.470 kg.Assume that the test is conducted with a significance level given by a = 0.05.a. What should we conclude about the
Birth Weights Use the data and the claim given in Exercise 1 to identify the null and alternative hypotheses and the test statistic. What is the sampling distribution of the test statistic?
Birth Weights Shown below are birth weights (in kilograms) of male babies born to mothers taking a special vitamin supplement (based on data from the New York State Department of Health). Assume that we want to use the sample data to test the claim that the sample is from a population with a
Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has a power of 0.4943 of supporting the claim that m 6 7 hours of sleep when the actual population mean is 6.0 hours of sleep.Interpret this value of the
Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. One approach is to approximate critical t values by calculating t = 2df # 1eA2>df - 12 where df = n - 1, e = 2.718, A = z18 # df + 32>18 # df + 12, and z is the
Diastolic Blood Pressure for Men Repeat the preceding exercise for adult males instead of adult females.
Diastolic Blood Pressure for Women Use the diastolic blood pressure measurements for adult females listed in Data Set 1 “Body Data” in Appendix B and test the claim that the adult female population has a mean diastolic blood pressure level less than 90 mm Hg. A diastolic blood pressure above 90
Pulse Rates Use the pulse rates of adult males listed in Data Set 1 “Body Data” in Appendix B to test the claim that the mean is less than 75 bpm. Use a 0.05 significance level.
Pulse Rates Use the pulse rates of adult females listed in Data Set 1 “Body Data” in Appendix B to test the claim that the mean is less than 75 bpm. Use a 0.05 significance level.
Heights of Supermodels Listed below are the heights (cm) for the simple random sample of female supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr, Kroes, Swanepoel, Prinsloo, Hosk, Kloss, Robinson, Heatherton, and Refaeli. Use a 0.01 significance level to test the claim that
Car Booster Seats The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard “head injury condition” units). The safety requirement is that the hic measurement
Got a Minute? Students of one of the authors estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds.Does it appear that
Lead in Medicine Listed below are the lead concentrations (in mg>g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India.The lead concentrations listed here are from medicines manufactured in the United States(based on data from “Lead, Mercury,
Treating Chronic Fatigue Syndrome Patients with chronic fatigue syndrome were tested, and then retested after being treated with fludrocortisone. A standard scale from -7 to +7 is used to measure fatigue before and after the treatment. The changes are summarized with these statistics: n = 21, x =
Course Evaluations Data from student course evaluations were obtained from the University of Texas at Austin. The summary statistics are n = 436, x = 3.97, s = 0.55. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00. Do the
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