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biostatistics
Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions
Football Player Weights Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the results likely to be representative of all National Football League (NFL)
Football Player Numbers Listed below are the jersey numbers of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. What do the results tell us?89 91 55 7 20 99 25 81 19 82 60
MCAT Score Listed below are mean MCAT scores listed in order by year, starting with the year 2002. What important feature of the data is not revealed by any of the measures of center?27.0 26.8 27.1 27.3 27.4 27.7 28.1 27.9 28.3 28.2 28.3 28.4
Charges for Births Data Set 3 “Births” in Appendix B includes total charges for births at four hospitals in New York State, and the top 10 highest amounts (in dollars) are listed below.What do the results tell us about the population of all such charges?471,062 359,091 290,837 271,863 255,788
Resistant Measures Here are five pulse rates (BPM) of females: 80, 94, 58, 66, 56. Find the mean and median of these five values. Then find the mean and median after including a sixth value of 740, which is an outlier. (One of the female pulse rates is 74, but 740 is used here as an error resulting
Measures of Center In what sense are the mean, median, mode, and midrange measures of “center”?
What’s Wrong? The Centers for Disease Control and Prevention (CDC) publishes a list of smoking rates in each state. If we add the 50 percentages and then divide by 50, we get 19.67%.Is the value of 19.67% the mean smoking rate for all of the United States? Why or why not?
Average A report includes a statement that the “average” Medical College Admission Test(MCAT) score of applicants to medical schools is 28.4. What is the role of the term average in statistics? Should another term be used in place of average?
Finding the Equation of the Regression Line. In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. X 10 8 13 9 11 14 6 4 12 7 5 y 7.46 6.77 12.74 7.11 7.81
Finding the Equation of the Regression Line. In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. X 10 8 13 9 11 14 6 4 12 7 5 y 9.14 8.14 8.74 8.77 9.26 8.10
Confidence Interval for Mean Predicted Value Example 1 in this section illustrated the procedure for finding a prediction interval for an individual value of y. When using a specific value x0 for predicting the mean of all values of y, the confidence interval is as follows:The critical value
Terminology Using the lengths (in.), chest sizes (in.), and weights (lb) of bears from Data Set 11 “Bear Measurements” in Appendix B, we get this regression equation: Weight =-274 + 0.426 Length + 12.1 Chest Size. Identify the response and predictor variables.
Best Multiple Regression Equation For the regression equation given in Exercise 1, the P-value is 0.000 and the adjusted R2 value is 0.925. If we were to include an additional predictor variable of neck size (in.), the P-value becomes 0.000 and the adjusted R2 becomes 0.933.Given that the adjusted
Adjusted Coefficient of Determination For Exercise 2, why is it better to use values of adjusted R2 instead of simply using values of R2?
Interpreting R2 For the multiple regression equation given in Exercise 1, we get R2 = 0.928. What does that value tell us?
Height of Son Identify the multiple regression equation that expresses the height of a son in terms of the height of his father and mother. Interpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons.
Height of Son Identify the following:a. The P-value corresponding to the overall significance of the multiple regression equationb. The value of the multiple coefficient of determination R2c. The adjusted value of R2 Interpreting a Computer Display. In Exercises 5–8, we want to consider the
Height of Son Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not? Interpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the
Height of Son A son will be born to a father who is 70 in. tall and a mother who is 60 in.tall. Use the multiple regression equation to predict the height of the son. Is the result likely to be a good predicted value? Why or why not? Interpreting a Computer Display. In Exercises 5–8, we want to
If only one predictor (x) variable is used to predict weight, which single variable is best? Why? Predicting Weights of Males. In Exercises 9–12, refer to the accompanying table, which was obtained by using the data for males in Data Set 1 “Body Data” in Appendix B. The response (y) variable
If exactly two predictor (x) variables are to be used to predict weight, which two variables should be chosen? Why? Predicting Weights of Males. In Exercises 9–12, refer to the accompanying table, which was obtained by using the data for males in Data Set 1 “Body Data” in Appendix B. The
Which regression equation is best for predicting the weight? Why? Predicting Weights of Males. In Exercises 9–12, refer to the accompanying table, which was obtained by using the data for males in Data Set 1 “Body Data” in Appendix B. The response (y) variable is weight (kg), and the
If a male has a height of 186 cm, a waist circumference of 107.8 cm, and an arm circumference of 37.0 cm, what is the best predicted weight? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Predicting Weights of Males. In Exercises 9–12,
Predicting Nicotine in Cigarettes Refer to Data Set 15 “Cigarette Contents” in Appendix B and use the tar, nicotine, and CO amounts for the cigarettes that are 100 mm long, filtered, nonmenthol, and nonlight (the last set of measurements). Find the best regression equation for predicting the
Predicting Nicotine in Cigarettes Repeat the preceding exercise using the sample data from the Menthol cigarettes listed in Data Set 15 in Appendix B. Appendix B Data Sets. In Exercises 13–16, refer to the indicated data set in Appendix B and use technology to obtain results.
Predicting IQ Score Refer to Data Set 9 “IQ and Brain Size” in Appendix B and find the best regression equation with IQ score as the response (y) variable. Use predictor variables of brain volume and>or body weight. Why is this equation best? Based on these results, can we predict someone’s
Full IQ Score Refer to Data Set 8 “IQ and Lead” in Appendix B and find the best regression equation with IQF (full IQ score) as the response (y) variable. Use predictor variables of IQV (verbal IQ score) and IQP (performance IQ score). Why is this equation best? Based on these results, can we
Testing Hypotheses About Regression Coefficients If the coefficient b1 has a nonzero value, then it is helpful in predicting the value of the response variable. If b1 = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation.To test
Confidence Intervals for Regression Coefficients A confidence interval for the regression coefficient b1 is expressed as b1 - E 6 b1 6 b1 + E where E = ta>2sb1 The critical t score is found using n - (k + 1) degrees of freedom, where k, n, and sb1 are described in Exercise 17.Using the sample data
Dummy Variable What is a dummy variable?
Logistic Regression What is the fundamental difference between logistic regression and linear regression?
Simple Logistic Regression How is simple logistic regression different from multiple logistic regression?
True or False Determine whether this statement is true or false: If a multiple regression equation has a continuous response variable and three predictor variables, including one that is a dummy variable, then we must use methods of logistic regression because a dummy variable is included.
Bears Identify the predictor and response variables. Which of these are dummy variables?In Exercises 5–8, use the following logistic regression equation found from Data Set 11 “Bear Measurements” in Appendix B. The value of p is the probability that the bear is male. P In == 2.40 - 0.0553
Bears The given regression equation has an overall P-value of 0.218. What does that suggest about the quality of predictions made using the regression equation?In Exercises 5–8, use the following logistic regression equation found from Data Set 11 “Bear Measurements” in Appendix B. The value
Bears Use a length of 60 in. and a weight of 300 lb to find the probability that the bear is a male. Also, what is the probability that the bear is a female?In Exercises 5–8, use the following logistic regression equation found from Data Set 11 “Bear Measurements” in Appendix B. The value of
Bears Use a length of 40 in. and a weight of 50 lb to find the probability that the bear is a male. What is the probability that the bear is a female? Considering the given length and weight, what do we know about this bear?In Exercises 5–8, use the following logistic regression equation found
Weight of a Bear Refer to Data Set 11 “Bear Measurements” in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) variable represent weight, use the variable of age and the dummy variable of sex to find the
Sex, Height, and Weight Refer to Data Set 1 “Body Data” in Appendix B and use the sex, height, and weight of the human subjects. Letting the response (y) variable represent weight, use the dummy variable of sex and use the height to find the multiple regression equation. Use the equation to
Sex, Height, and Weight Refer to Data Set 1 “Body Data” in Appendix B and use the sex, height, and weight of the human subjects. Letting the response (y) variable represent sex(0 = female, 1 = male), use the variables of height and weight to find the multiple regression equation. Use the
Sex, Height, and Pulse Rate Refer to Data Set 1 “Body Data” in Appendix B and use the sex, height, and pulse rate of the human subjects. Letting the response (y) variable represent sex(0 = female, 1 = male), use the variables of height and pulse rate to find the multiple regression equation.
Sex, Foot Length, and Height Refer to Data Set 7 “Foot and Height” in Appendix B and use the sex, foot length, and height of the subjects. Letting the response (y) variable represent sex (0 = female, 1 = male), use the variables of foot length and height to find the multiple regression
Sex, Shoe Size, and Height Refer to Data Set 7 “Foot and Height” in Appendix B and use the sex, shoe size, and height of the subjects. Letting the response (y) variable represent sex(0 = female, 1 = male), use the variables of shoe size and height to find the multiple regression equation. Use
Conclusion The linear correlation coefficient r is found to be 0.867, the P-value is 0.057, and the critical values for a 0.05 significance level are {0.878. If you are using a 0.05 significance level, what should you conclude?
2. Switched Variables Which of the following change if the two variables of right arm and left arm blood pressure measurements are switched: the value of r = 0.867, the P-value of 0.057, the critical values of {0.878?
3. Change in Scale Exercise 1 stated that r is found to be 0.867. How does the value of r change if the scale for the right arm measurements is changed from mm Hg to in. Hg, so that all of the values for the right arm are multiplied by 0.0394?
4. Values of r If you had computed the value of the linear correlation coefficient to be 1.500, what should you conclude?
5. Predictions The sample data result in a linear correlation coefficient of r = 0.867 and the regression equation yn = 43.6 + 1.31x. What is the best predicted value for the left arm given that the measurement for the right arm is 100 mm Hg?
6. Predictions Repeat the preceding exercise, assuming that the linear correlation coefficient for the paired sample data is r = 0.997.
7. Explained Variation Given that the linear correlation coefficient r is found to be 0.867, what is the proportion of the variation in left arm measurements that is explained by the relationship between the right and left arm measurements?
8. Linear Correlation and Relationships True or false: If there is no linear correlation between right arm measurements and left arm measurements, then those two variables are not related in any way.
9. Causality True or false: If the sample data lead us to conclude that there is sufficient evidence to support the claim of a linear correlation between right and left arm measurements, then we could also conclude that increases in right arm measurements cause increases in left arm measurements.
10. Interpreting Scatterplot If the sample data were to result in the scatterplot shown here, what is the value of the linear correlation coefficient r?
Hospital Cybersecurity The table below lists leading digits of 317 inter-arrival Internet traffic times for a hospital computer along with the frequencies of leading digits expected with Benford’s law.a. Identify the notation used for observed and expected values.b. Identify the observed and
Using Yates’s Correction for Continuity The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates’s correction for continuity in cells with an expected frequency of less than 10 or in all cells of a contingency table
Given that the P-value for the hypothesis test is 0.0000 when rounded to four decimal places, what do you conclude? What do the results indicate about the rule that women and children should be the first to be saved?
What distribution is used to test the stated claim (normal, t, F, chi-square, uniform)?
Identify the null and alternative hypotheses corresponding to the stated claim.
Given that the P-value for the hypothesis test is 0.501, what do you conclude? Does it appear that the heights were obtained through measurement or that the subjects reported their heights?
If using a 0.05 significance level to test the stated claim, find the number of degrees of freedom.
Is the hypothesis test left-tailed, right-tailed, or two-tailed?
When testing the claim in Exercise 1, what are the observed and expected frequencies for the last digit of 7?
What are the null and alternative hypotheses corresponding to the stated claim?
Equivalent Tests A x2 test involving a 2 * 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-1. Using the claim and table in Exercise 5 “Splint or Surgery?” verify that the x2 test statistic and the z test statistic (found from the test of
Baseball Player Births In his book Outliers, author Malcolm Gladwell argues that more American-born baseball players have birthdates in the months immediately following July 31 because that was the age cutoff date for nonschool baseball leagues. The table below lists months of births for a sample
Injuries and Motorcycle Helmet Color A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the table below(based on data from “Motorcycle
Clinical Trial of Echinacea In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of
Is Seat Belt Use Independent of Cigarette Smoking? A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock, American Journal of Public Health, Vol.
Clinical Trial of Lipitor Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. This is the largest-selling drug in the world, with $13 billion in sales for a recent year. Adverse reactions have been studied in clinical trials, and the table below
Clinical Trial of Campral Campral (acamprosate) is a drug used to help patients continue their abstinence from the use of alcohol. Adverse reactions of Campral have been studied in clinical trials, and the table below summarizes results for digestive system effects among patients from different
Unusual Patient Deaths Alert nurses at the Veteran’s Affairs Medical Center in Northampton, Massachusetts, noticed an unusually high number of deaths at times when another nurse, Kristen Gilbert, was working. Those same nurses later noticed missing supplies of the drug epinephrine, which is a
Texting and Seat Belt Use In a study of high school students at least 16 years of age, researchers obtained survey results summarized in the accompanying table (based on data from“Texting While Driving and Other Risky Motor Vehicle Behaviors Among U. S. High School Students,” by O’Malley,
Is the Vaccine Effective? In a USA Today article about an experimental vaccine for children, the following statement was presented: “In a trial involving 1602 children, only 14 (1%)of the 1070 who received the vaccine developed the flu, compared with 95 (18%) of the 532 who got a placebo.” The
Clinical Trial of Chantix Chantix (varenicline) is a drug used as an aid for those who want to stop smoking. The adverse reaction of nausea has been studied in clinical trials, and the table below summarizes results (based on data from Pfizer). Use a 0.01 significance level to test the claim that
Lie Detector The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H.Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table
Can Dogs Detect Cancer? An experiment was conducted to test the ability of dogs to detect bladder cancer. Dogs were tested with urine samples from bladder cancer patients and people in a control group who did not have bladder cancer. Results are given in the table below (based on data from the New
Tooth Fillings and Sensory Disorders In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which include mercury. The table below shows results from a study in which some patients were treated with amalgam restorations and others were treated
Tooth Fillings and Adverse Health Conditions The table below shows results from a study in which some dental patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury (based on data from “Neuropsychological and Renal Effects of
Texting and Drinking In a study of high school students at least 16 years of age, researchers obtained survey results summarized in the accompanying table (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U. S. High School Students,”by O’Malley, Shults,
Splint or Surgery? A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below (based on data from “Splinting vs. Surgery in the Treatment of Carpal Tunnel Syndrome,” by
Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.
Hypothesis Test The accompanying TI-83>84 Plus calculator display results from the hypothesis test described in Exercise 1.Assume that the hypothesis test requirements are all satisfied. Identify the test statistic and the P-value (expressed in standard form and rounded to three decimal places),
Hypotheses Refer to the data given in Exercise 1 and assume that the requirements are all satisfied and we want to conduct a hypothesis test of independence using the methods of this section. Identify the null and alternative hypotheses.
Handedness and Cell Phone Use The accompanying table is from a study conducted with the stated objective of addressing cell phone safety by understanding why we use a particular ear for cell phone use. (See “Hemispheric Dominance and Cell Phone Use,” by Seidman, Siegel, Shah, and Bowyer, JAMA
Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data”in Appendix B for the heights of females.Height (cm) Less than 155.45 155.45 - 162.05 162.05 - 168.65 Greater than 168.65 Frequencya. Enter the observed frequencies in the table above.b. Assuming a normal
Discharges After Birth Data Set 3 “Births” includes the days of the weeks that newborn babies were discharged from the hospital. A hospital administrator claims that such discharges occur on the seven different days of the week with equal frequency. Use a 0.01 significance level to test that
Admissions for Birth Data Set 3 “Births” includes the days of the weeks that prospective mothers were admitted to a hospital to give birth. A physician claims that because many births are induced or involve cesarean section, they are scheduled for days other than Saturday or Sunday, so births
CT Scan When analyzing the leading digits of the magnitudes of gradients from a CT image, the frequencies were found to be 83, 58, 27, 21, 21, 21, 6, 4, 9, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. Use a 0.01 significance level to test for
MRI When analyzing the leading digits of the magnitudes of gradients from an MRI (magnetic resonance image) of a patient, the frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. Use a
Mendelian Genetics Experiments are conducted with hybrids of two types of peas. If the offspring follow Mendel’s theory of inheritance, the seeds that are produced are yellow smooth, green smooth, yellow wrinkled, and green wrinkled, and they should occur in the ratio of 9:3:3:1, respectively. An
Bias in Clinical Trials Researchers investigated the issue of race and equality of access to clinical trials. The table on the top of the next page shows the population distribution and the numbers of participants in clinical trials involving lung cancer (based on data from “Participation in
Genotypes Based on the genotypes of parents, offspring are expected to have genotypes distributed in such a way that 25% have genotypes denoted by AA, 50% have genotypes denoted by Aa, and 25% have genotypes denoted by aa. When 145 offspring are obtained, it is found that 20 of them have AA
Eye Color A researcher has developed a theoretical model for predicting eye color. After examining a random sample of parents, she predicts the eye color of the first child. The table below lists the eye colors of offspring. On the basis of her theory, she predicted that 87% of the offspring would
Genetics The Advanced Placement Biology class at Mount Pearl Senior High School conducted genetics experiments with fruit flies, and the results in the following table are based on the results that they obtained. Use a 0.05 significance level to test the claim that the observed frequencies agree
Baseball Player Births In his book Outliers, author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool baseball leagues. Here is a sample of frequency counts of months of birthdates of
Flat Tire and Missed Class A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to
Motorcycle Fatalities Randomly selected deaths of motorcycle riders are summarized in the table below (based on data from the Insurance Institute for Highway Safety). Use a 0.05 significance level to test the claim that such fatalities occur with equal frequency in the different months. How might
Deaths from Car Crashes Randomly selected deaths from car crashes were obtained, and the results are included in the table below (based on data from the Insurance Institute for Highway Safety). Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on
Occupational Injuries Randomly selected non-fatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred, and the results are listed below (based on data from the Bureau of Labor Statistics). Use a 0.05 significance level to test the claim that
Hospital Cybersecurity What do the results from the preceding exercises suggest about the possibility that the computer has been hacked? Is there any corrective action that should be taken?
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