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biostatistics
Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions
Biodiversity Find the values of x1 (the number of women who were aware of the statement), x2 (the number of men who were aware of the statement), pn 1, pn 2, and the pooled proportion p obtained when testing the claim given in Exercise 1.
Biodiversity Identify the null and alternative hypotheses resulting from the claim that for the people who were aware of the statement, the proportion of women is equal to the proportion of men.
Finding Lower Critical F Values For hypothesis tests that are two-tailed, the methods of Part 1 require that we need to find only the upper critical value. Let’s denote the upper critical value by FR, where the subscript indicates the critical value for the right tail. The lower critical value FL
Levene-Brown-Forsythe Test Repeat Exercise 16 “Blanking Out on Tests” using the Levene-Brown-Forsythe test.
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 its effect on anxiety. The following scores are measures of “debilitating test anxiety,” which most
Longevity Listed below are the numbers of years that popes and British monarchs (since 1690) lived after their election or coronation. Treat the values as simple random samples from a larger population. Use a 0.05 significance level to test the claim that both populations of longevity times have
Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S.
Body Temperatures of Men and Women Listed below are the body temperatures ( F) measured in males at 8 AM on Day 2 as listed in Data Set 2 “Body Temperatures” in Appendix B.For the body temperatures of females measured at the same time, we get n = 59, x = 97.45 F, and s = 0.66 F. Use a 0.05
Zinc Treatment Use a 0.05 significance level to test the claim that weights of babies born to mothers given placebos vary more than weights of babies born to mothers given zinc supplements.Use the following statistics (based on data from “The Effect of Zinc Supplementation on Pregnancy
Cigarette Filters and Nicotine Listed below are statistics from measured nicotine contents of randomly selected filtered and non-filtered king-size cigarettes (based on data from the Federal Trade Commission). Use a 0.05 significance level to test the claim that king-size cigarettes with filters
Humidity in Treating Croup In a randomized controlled trial conducted with children suffering from viral croup, 46 children were treated with low humidity while 46 other children were treated with high humidity. Researchers used the Westley Croup Score to assess the results after one hour. The
Magnet Treatment of Pain Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and
IQ and Lead Exposure Data Set 8 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below. Use a 0.05 significance level to
Baseline Characteristics In journal articles about clinical experiments, it is common to include baseline characteristics of the different treatment groups so that they can be compared.In an article about the effects of different diets, a table of baseline characteristics showed that 40 subjects
Second-Hand Smoke Data Set 14 “Passive and Active Smoke” includes cotinine levels measured in a group of smokers (n = 40, x = 172.48 ng>mL, s = 119.50 ng>mL)and a group of nonsmokers not exposed to tobacco smoke (n = 40, x = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine,
Testing Effects of Alcohol Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a
Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?
Testing Normality For the hypothesis test described in Exercise 2, the sample sizes are n1 = 147 and n2 = 153.When using the F test with these data, is it correct to reason that there is no need to check for normality because n1 7 30 and n2 7 30?
F Test If using the sample data in Data Set 1 “Body Data” in Appendix B for a test of the claim that heights of men and heights of women have different variances, we find that s = 7.48296 cm for women and s = 7.10098 cm for men.a. Find the values of s21 and s22 and express them with appropriate
F Test Statistica. If s21 represents the larger of two sample variances, can the F test statistic ever be less than 1?b. Can the F test statistic ever be a negative number?c. If testing the claim that s21 s22, what do we know about the two samples if the test statistic F is very close to 1.d. Is
Bootstrapa. If paired sample data (x, y) are such that the values of x do not appear to be from a population with a normal distribution, and the values of y do not appear to be from a population with a normal distribution, does it follow that the values of d will not appear to be from a population
Body Temperatures Refer to Data Set 2 “Body Temperatures” in Appendix B and use all of the matched pairs of body temperatures at 8 AM and 12 AM on Day 1.When using a 0.05 significance level for testing a claim of a difference between the temperatures at 8 AM and at 12 AM on Day 1, how are the
Tobacco and Alcohol in Children’s Movies Refer to Data Set 13 “Alcohol and Tobacco in Movies” in Appendix B and use the times (seconds) that animated Disney movies showed the use of tobacco and the times that they showed the use of alcohol. Use a 0.05 significance level to test the claim that
Heights of Fathers and Sons Repeat Exercise 10 “Heights of Fathers and Sons” using all of the heights of fathers and sons listed in Data Set 6 “Family Heights” in Appendix B. Larger Data Sets. In Exercises 17–20, use the indicated Data Sets from Appendix B.The complete data sets can be
Heights of Mothers and Daughters Repeat Exercise 9 “Heights of Mothers and Daughters”using all of the heights of mothers and daughters listed in Data Set 6 “Family Heights” in Appendix B. Larger Data Sets. In Exercises 17–20, use the indicated Data Sets from Appendix B.The complete data
Body Temperatures Repeat Exercise 7 “Body Temperatures” using all of the 8 AM and 12 AM body temperatures on Day 2 as listed in Data Set 2 “Body Temperatures” in Appendix B.Use a significance level of 0.05. Larger Data Sets. In Exercises 17–20, use the indicated Data Sets from Appendix
Historical Data Set In 1908, “Student” (William Gosset) published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of straw seed (regular and kiln dried) that were used on adjacent plots of land. The listed
Self-Reported and Measured Male Heights As part of the National Health and Nutrition Examination Survey, the Department of Health and Human Services obtained self-reported heights (in.) and measured heights (in.) for males aged 12–16. Listed below are sample results.Construct a 99% confidence
Hypnotism for Reducing Pain A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table (based on “An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia,” by Price and
Two Heads Are Better Than One Listed below are brain volumes (cm3) of twins from Data Set 9 “IQ and Brain Size” in Appendix B. Construct a 99% confidence interval estimate of the mean of the differences between brain volumes for the first-born and the second-born twins. What does the confidence
Before , After Treatment Results Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data
Friday the 13th 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 and Fridays on the following 13th of the same month (based on data from “Is Friday the 13th Bad for Your Health?”
Heights of Fathers and Sons Listed below are heights (in.) of fathers and their first sons. The data are from a journal kept by Francis Galton. (See Data Set 6 “Family Heights”)Use a 0.05 significance level to test the claim that there is no difference in heights between fathers and their first
Heights of Mothers and Daughters Listed below are heights (in.) of mothers and their first daughters. The data are from a journal kept by Francis Galton. (See Data Set 6 “Family Heights.”) Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and
The Spoken Word Listed below are the numbers of words spoken in a day by each member of six different couples.a. Use a 0.05 significance level to test the claim that among couples, males speak fewer words in a day than females.b. Construct the confidence interval that could be used for the
Body Temperatures Listed below are body temperatures from seven different subjects measured at two different times in a day (from Data Set 2 “Body Temperatures” in Appendix B).a. Use a 0.05 significance level to test the claim that there is no difference between body temperatures measured at 8
Heights of Presidents A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed below are heights (cm) of presidents along with the heights of their main opponents.a. Use the sample data with a 0.05 significance level to test the claim
Is Blood Pressure the Same for Both Arms? Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman (based on data from “Consistency of Blood Pressure Differences Between the Left and Right Arms,” by Eguchi et al., Archives of Internal
Degrees of Freedom If we use the sample data in Exercise 2 for constructing a 99% confidence interval, what is the number of degrees of freedom that should be used for finding the critical value of ta>2? What is the critical value ta>2?
Units of Measure If the values listed in Exercise 2 are changed so that they are expressed in Celsius degrees instead of Fahrenheit degrees, how are hypothesis test results affected?
Notation Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM (from Data Set 2 “Body Temperatures”). Find the values of d and sd. In general, what does md represent?Temperature 1 F2 at 8 AM 97.8 99.0 97.4 97.4 97.5 Temperature 1 F2 at 12 AM 98.6
True Statements? For the methods of this section, which of the following statements are true?a. When testing a claim using a simple random sample of ten matched pairs of heights, hypothesis tests using the P-value method, critical value method, and confidence interval method will all result in the
No Variation in a Sample An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication
Degrees of Freedom In Exercise 20 “Blanking Out on Tests,” using the “smaller of n1 - 1 and n2 - 1” for the number of degrees of freedom results in df = 15.Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by
Pooling Repeat Exercise 15 “IQ and Lead Exposure” by assuming that the two population standard deviations are equal, so s1 = s2. Use the appropriate method from Part 2 of this section.Does pooling the standard deviations yield results showing greater significance?
Birth Weights Refer to Data Set 3 “Births” and use the birth weights of boys and girls.Test the claim that at birth, girls have a lower mean weight than boys.
Do Men and Women Have the Same Mean Diastolic Blood Pressure? Refer to Data Set 1 “Body Data” and use a 0.05 significance level to test the claim that women and men have the same mean diastolic blood pressure.
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 its effect on anxiety. The following scores are measures of “debilitating test anxiety,” which most
Longevity Listed below are the numbers of years that popes and British monarchs (since 1690) lived after their election or coronation (based on data from Computer-Interactive Data Analysis, by Lunn and McNeil, John Wiley & Sons). Treat the values as simple random samples from a larger population.a.
Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S.
Bad Stuff in Children’s Movies Data Set 13 “Alcohol and Tobacco in Movies” includes lengths of times (seconds) of tobacco use shown in animated children’s movies. For the Disney movies, n = 33, x = 61.6 sec, s = 118.8 sec. For the other movies, n = 17, x = 49.3 sec, s = 69.3 sec. The sorted
Seat Belts A study of seat belt use involved children who were hospitalized after motor vehicle crashes. For a group of 123 children who were wearing seat belts, the number of days in intensive care units (ICU) has a mean of 0.83 and a standard deviation of 1.77. For a group of 290 children who
IQ and Lead Exposure Data Set 8 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below.a. Use a 0.05 significance level
BMI We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person’s body mass index(BMI) is computed by dividing weight (kg) by the square of height (m). Given below are the BMI statistics for random
Second-Hand Smoke Data Set 14 “Passive and Active Smoke” includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, x = 60.58 ng>mL, s = 138.09 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, x = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is
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 heavy users of marijuana in college were tested for memory recall, with the results given below (based on data from “The
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 people who drank ethanol and another group given a placebo. The results are shown in the accompanying table(based on data from
Bipolar Depression Treatment In clinical experiments involving different groups of independent samples, it is important that the groups be similar in the important ways that affect the experiment. In an experiment designed to test the effectiveness of paroxetine for treating bipolar depression,
Cigarette Tar The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered 100-mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg(from Data Set 15
Magnet Treatment of Pain People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given
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 object assembly skill, which was described as “a task requiring visual-spatial skills related to mathematical competence.”
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.“Days of fever” was one criterion used to measure effects. Among 337 children treated with echinacea, the mean number
Hypothesis Test of Effectiveness of Humidity in Treating Croup In a randomized controlled trial conducted with children suffering from viral croup, 46 children were treated with low humidity while 46 other children were treated with high humidity. Researchers used the Westley Croup Score to assess
Degrees of Freedom For Example 1 on page 409, we used df = smaller of n1 - 1 and n2 - 1, we got df = 39, and the corresponding critical value is t = 1.685. If we calculate df using Formula 9-1, we get df = 76.423, and the corresponding critical value is t = 1.665.How is using a critical value of t
Hypothesis Tests and Confidence Intervals for Hemoglobina. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the
Confidence Interval for Hemoglobin Large samples of women and men are obtained and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures
Independent and Dependent Samples Which of the following involve independent samples?a. Data Set 2 “Body Temperatures” includes body temperatures of subjects measured at 8 AM and again at 12 AM on Day 1 of observation.b. Data Set 6 “Family Heights” includes heights of fathers and heights of
Audiometry Confidence level is 95%, s is not known, and the normal quantile plot of measured right-ear hearing thresholds from 10 randomly selected adult females is shown on the top of the next page. 1.5 20 12 08 04 2 z score -0.4 0.8 12 10 B 11 F 10 X Values 2 13 14 15
Vision Confidence level is 90%, s is not known, and the histogram of right-eye vision measurements is obtained from a random sample of 61 adult males. Frequency 50 40- 30 25 30 75 125 150 125 200 Vision in Right Eye
Brain Volume Using all of the brain volumes listed in Data Set 9 “IQ and Brain Size,” we get this 95% confidence interval estimate: 9027.8 6 s2 6 33,299.8, and the units of measurement are (cm3)2. Identify the corresponding confidence interval estimate of s and include the appropriate units.
Expressing Confidence Intervals Example 2 showed how the statistics of n = 22 and s = 14.3 result in this 95% confidence interval estimate of s: 11.0 6 s 6 20.4. That confidence interval can also be expressed as (11.0, 20.4), but it cannot be expressed as 15.7 { 4.7.Given that 15.7 { 4.7 results in
Last Digit Analysis The accompanying dotplot depicts the last digits of the weights of 153 males in Data Set 1 “Body Data.” Do those digits appear to be from a normally distributed population? If not, does the large sample size of n = 153 justify treating the values as if they were from a
Normality Requirement What is different about the normality requirement for a confidence interval estimate of s and the normality requirement for a confidence interval estimate of m?
Nicotine in Menthol Cigarettes 95% confidence; n = 25, s = 0.24 mg. Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2 R, and the confidence interval estimate of S. The samples are
White Blood Cell Counts of Men 95% confidence; n = 153, s = 1.86. Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2 R, and the confidence interval estimate of S. The samples are
Platelet Counts of Women 99% confidence; n = 147, s = 65.4. Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2 R, and the confidence interval estimate of S. The samples are from
Heights of Men 99% confidence; n = 153, s = 7.10 cm. Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2 R, and the confidence interval estimate of S. The samples are from Appendix
Body Temperature Data Set 2 “Body Temperatures” in Appendix B includes a sample of 106 body temperatures having a mean of 98.20 F and a standard deviation of 0.62 F (for day 2 at 12 AM). Construct a 95% confidence interval estimate of the standard deviation of the body temperatures for the
Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss
Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. After treatment with zopiclone, 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from “Cognitive Behavioral
Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg>dL)had a mean of
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 as it is affectionately called). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these
Queues A Providence Hospital experiment involves two different waiting line configurations for patients arriving for admission. The waiting times (in seconds) are recorded with a single-line configuration that feeds four stations and another configuration with individual lines at the four stations.
Shoveling Heart Rates Because cardiac deaths appear to increase after heavy snowfalls, an experiment was designed to compare cardiac demands of snow shoveling to those of using an electric snow thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats per
Acupuncture for Migraines In a study designed to test the effectiveness of acupuncture for treating migraine headaches, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a
Birth Length of Stay Refer to Data Set 3 “Births” in Appendix B.a. Use the lengths of stay (days) for the 205 girls to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained. For critical values, use x2 L = 166.337 and x2 R =
Birth Weights Refer to Data Set 3 “Births” in Appendix Ba. Use the 205 birth weights of girls to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained. For critical values, use x2 L = 166.337 and x2 R = 245.449.b. Repeat part
IQ of Biostatistics Professors You want to estimate s for the population of IQ scores of biostatistics professors. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of s. Is this sample size practical?
ER Waiting Times You want to estimate s for the population of waiting times for hospital emergency rooms. You want to be 99% confident that the sample standard deviation is within 1% of s. Find the minimum sample size. Is this sample size practical?
Statistics Student Incomes You want to estimate the standard deviation of the annual incomes of all current statistics students. Find the minimum sample size needed to be 95% confident that the sample standard deviation is within 20% of the population standard deviation.Are those incomes likely to
Aspirin Quality When attempting to verify the aspirin contents in manufactured tablets, you must estimate the standard deviation of the population of aspirins in use. Find the minimum sample size needed to be 99% confident that the sample standard deviation is within 10%of the population standard
Finding Critical Values In constructing confidence intervals for s or s2, Table A-4 can be used to find the critical values x2 L and x2 R only for select values of n up to 101, so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate x2 L
Finding Sample Size Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation s, the following formula can be used:where za>2 corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95%
Replacement Why does the bootstrap method require sampling with replacement? What would happen if we used the methods of this section but sampled without replacement?
Bootstrap Sample Here is a random sample of numbers of patients in a day who required medication at a clinic: 12, 19, 13, 43, 15.For this sample, what is a bootstrap sample?
Bootstrap Sample Given the sample data from Exercise 2, which of the following are not possible bootstrap samples?a. 12, 19, 13, 43, 15b. 12, 19, 15c. 12, 12, 12, 43, 43d. 14, 20, 12, 19, 15e. 12, 13, 13, 12, 43, 15, 19
How Many? The examples in this section all involved no more than 20 bootstrap samples.How many should be used in real applications?
Survey Responses In a physician’s office, four patients are asked if they would be willing to complete a survey before leaving. Responses included these: no, yes, no, no. Letting “yes”= 1 and letting “no” = 0, here are ten bootstrap samples for those responses: {0, 0, 0, 0},{1,¤ 0, 1,
ER Admissions An emergency room official records whether patients are admitted to the hospital, and the results include these: admitted, admitted, not admitted, not admitted. Letting“admitted” = 1 and letting “not admitted” = 0, here are ten bootstrap samples for these patients:{0, 0, 0,
Freshman 15 Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 10 “Freshman 15” in Appendix B): 11, 3, 0, -2, where -2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples:{11, 11, 11, 0},
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