Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file Ch a Chapter Introduction 1-2 Types of Data In Exercises – 4, determine whether the given value is a statistic or a parameter Statistic, since 12 males (the sample size of males) is a characteristic of a sample Statistic, since 3.8 (the sample mean) is a characteristic of a sample of Canadian geese Statistic, since 226 m (the sample mean) is a characteristic of a sample of frigate birds Parameter, since 2.7 years (the population mean) is a characteristic of the population of cloned sheep In Exercises – 8, determine whether the given values are from a discrete or continuous data set Discrete, since the number of birds must be in the form of whole numbers, a fraction of a bird is not possible Continuous, since length in inches of hummingbirds can take on any value over a continuous span Discrete, since the number of families having guns in their homes must be in the form of whole numbers; a fraction of a home is not possible Continuous, since head width in inches can take on any value over a continuous span In Exercises – 16, determine which of the four levels of measurement (nominal, ordinal, interval ratio) is most appropriate Ratio, since there are equal intervals and a natural starting point of inches 10 Ordinal, since racing ability can be ordered low to high, but the actual difference in ability between the observed points cannot be determined 11 Interval, since body temperatures, either measured on a Fahrenheit or Centigrade scale, have equal intervals, but not have a natural starting point of 12 Nominal, since case numbers would be like labels, they identify but have no ordered property If the case numbers were in sequence of when they happened over time, they might have an ordinal property 13 Nominal, since the measure is used as a label for a category and the category does not have any ordinal property 14 Nominal, since social security numbers are labels with not orderable property 15 Ratio, since the number of manatees killed by boats has a natural starting point 16 Nominal, since zip codes are like labels and they have no ordered property There is a systematic way of assigning them, but that does not provide a way to order them in any way that would be meaningful In Exercises 17 – 20, identify the (a) sample and (b) population Also determine whether the sample is likely to be representative of the population 17 This would be a sample that is likely not representative of the population of rainbow trout, but it could be representative of rainbow trout in the stream where she is netting the trout Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file 2at./ Chapter 1: Introduction 18 This would be a sample that is likely not representative of the population of persons with attitudes or perceptions about health, but it might be representative of those who read the Florida newspaper 19 This would be a sample that would likely be representative of a population from which the sample was drawn 20 This would be a sample that is likely not representative of adult Americans, but it might be representative of the persons the graduate student knows 1-3 Design of Experiments In Exercises – 4, determine whether the given description corresponds to an observational study or an experiment Drug Testing Experiment, since the patients are being treated or exposed to a treatment, in this case Lipitor Treating Syphilis Observation, since patients are observed to determine health condition, but not treated in such a way to modify them However, this could be part of an experiment if they are compared on the same outcome variables with a treated group Quality Control Observation, since the amount of aspirin is observed in each tablet, they are not exposed to any treatment Magnetic Bracelets Experiment, since the use of the bracelets is a treatment that may result in lower likelihood of suffering from the effects of motion sickness In Exercises – 8, identify the type of observational study (cross-sectional, retrospective, prospective) Medical Research Retrospective, since the study focus is on what has happened in a period of the past (five years) for head injury patients Psychology of Trauma Prospective, since the study focus is on what happens to siblings of victims of the World Trade Center attacks in a period after the attacks occurred Flu Incidence Cross-sectional, since the study focus is on what happened at a specific time period Deer Encounters Retrospective, since the study focus is on what happened relative to damage caused by vehicles hitting deer in a period of the past (10 years) In Exercises – 20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster Aspirin Usage Convenience, since the researcher asks those who enter the clinic for treatment 10 Health Survey Selection Systematic, since every ith, in this case every thousandth, name/person in a list is selected for the sample 11 Telephone Polls Random, since telephone survey respondents were selected at random from a list of phone numbers; each phone number would have the same chance of being selected However, we need to exercise some caution in calling this random When a large majority of potential survey respondents had phones and researchers had access to the phone numbers, these types of surveys were often considered random However, with changes like “no call lists”, unlisted numbers, phones that can be programmed to screen out unrecognized calls, and individuals who have made cell phones their phone of choice and have dropped land line phones, random dialing of phone numbers is less likely to provide a representative sample than has been the case in the past Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file Ch a 12 Diet Stratified, since categories or strata are identified (four age strata) and 200 study participants are randomly selected from within each strata 13 Student Drinking Cluster, since classes form the clusters and clusters are randomly selected and all members of the selected clusters become study participants 14 Clinical Trial of Blood Treatment Random, since each of the treated subjects has the same chance of being selected for the sample that will receive the increased dosage 15 Sobriety Checkpoint Systematic, since every ith, in this case every fifth, driver is stopped for a sobriety check sample 16 Orange You Sweet Cluster, since each tree represents a cluster and 20 clusters are randomly selected and all the oranges for the cluster are measured for sugar content 17 Education and Health Stratified, since categories or strata are identified (three education level strata) and 150 survey participants are randomly selected from within each strata 18 Anthropometrics Convenience, since family members are selected since they just happen to be around to be interviewed and they are not selected from any larger group 19 Medical Research Cluster, since each hospital represents a cluster and 30 clusters are randomly selected and all the cardiac patients in the cluster are surveyed 20 AIDS Survey Stratified, since categories or strata are identified (four marital status strata) and 500 survey respondents are randomly selected from within each strata Exercises 21 – 26 relate to random samples and simple random samples 21 Sampling Aspirin Tablets Simple random sample, since every possible sample of size 50 has the same chance of being chosen 22 Sampling Students Random sample, since each student has the same chance of being selected, but every possible sample of five students (the number in each row) does not have the same chance of being selected for the sample 23 Convenience Sample Neither a random nor simple random sample, since random selection is not done in any way to select the sample 24 Systematic Sample Random, since each thermometer has the same chance of being selected, but not every possible sample has the same chance of being selected since the way this is done, the thermometers between those selected cannot be in included in a different sample 25 Stratified Sample Simple random sample, since we would assume that within each group, there is a random selection of possible survey respondents whereby every possible sample of size 100 men and 100 women has an equal chance of being selected 26 Type of Sampling Stratified, since there is an equal across group balance of sex and race participants This would not have been very likely, although possible, to have achieved this balance totally at random if a random sampling strategy had been used 27 Cluster Sample Random sample, since the blocks are randomly selected in such a way that all different combinations of 10 blocks would have an equal chance of being selected so relative to blocks this would be a simple random sample However since the blocks are made up of subjects who must remain within the blocks, there is no equal chance for any of the possible samples of all the residents to be selected Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file 4at./ Chapter 1: Introduction 28 Random Selection This would be a randomly selected voter However, this voter would not likely to representative of the state let alone the nation 29 Sample Design The study is prospective since subjects will be observed over a period of time after treatment introduction It is a randomized study if participants were randomly selected from a population and then randomly assigned into one of the three treatment conditions The study is double-blind when neither the treatment recipients nor those who administer the treatments know what treatment any participant receives The study is placebo-controlled when there is a control comparison group where the participants in that group receive a treatment that is expected to have no affect on levels of the outcome or dependent variable, but they are lead to believe they are receiving a treatment 30 Drivers with Cell Phones The problems relate to the notion of confounding where the groups to be compared are different or not equivalent in many ways such that the treatment gets mixed in with other factors to make the results un-interpretable Among these are: some in the group without cell phones might use them if they had them, some in the cell phone group might not use the cell phone while driving, the groups might differ on driving habits, the groups might differ in where they drive or how much they drive, and the groups might differ in other aspects like socio-economic or employment positions 31 Motorcycle Helmets The very important group that was not able to testify would be those who did not survive an accident whether or not they were using a helmet Review Exercises Sampling No, they cannot be considered representative of the population of the US since only those who were Internet subscribers were included, those without an Internet connection did not have the opportunity to respond In addition, those who responded to the survey self-selected themselves to so and thus were not even representative of all Internet subscribers Sampling Design A random sample could be used if all phone numbers in the US were entered into a computerized data base and phone numbers are selected at random (this would assume, a very questionable assumption, most members of the population have phones and their phone numbers are available) A systematic sample would be to select every ith phone number in the list, say every 10,000th phone number in the computerized data base A convenience sample would be used when an interviewer stopped adults walking through a mall and asked them whether they used Prilosec A stratified sample would be used when possible participants were identified as being in different age groups or gender groups and subjects selected at random within each group A cluster sample would be used when physicians are identified and they are randomly selected and all of the adult patients of the selected physicians are survey about using Prilosec Level of Measurement a Ratio, since there is a natural zero point and each pound or kilogram is equivalent b Ordinal, since the categories have order, but there is no basis for determining meaningful differences between the categories c Nominal, since the observation is a category with no order to the categories d Interval, since the observation is in equal units of years, but the zero point does not represent the beginning of the scale Salk Vaccine a Discrete, since children are measured as whole numbers, fractions of children are not possible b Ratio, since there is a natural zero point and each child is equivalent c Statistic, since the average is a measure based on a sample selected from the larger population d This could be a very emotional situation where parents whose children developed polio might feel they did not receive an effective treatment because they were assigned to a control situation and their children were deprived of receiving an effective preventive treatment There could easily be respondent bias resulting from what happened with their children in the study Those more likely to respond to the survey would be those with strong feelings one way or another Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file Ch a 5 Smokers a Systematic sample, this sample would likely be representative of all who smoke b Convenience sample, this sample would only represent those who are runners, not the population of all who smoke, so it would not be representative c Cluster sample, this sample would likely not be representative since the grocery stores may not be representative of grocery stores where smokers live d Random sample, this sample would be likely be representative of all who smoke e Stratified sample, this sample would likely not be representative since there are probably different distributions of smokers in varying zip codes Design of Experiments a Blinding relates to the study participants not being informed about the nature of the treatment that they are receiving In this study, the participants are not informed about whether they are receiving Sleepeze or something other than Sleepeze that is not expected to have any affect on insomnia b It is important to use blinding to balance any participant expectations that the treatment will have the affect intended Since participants are likely to be asked if the drug had an intended effect, we don’t want participants to know that the treatment they received was not expected to have any affect This would be an example of confounding c A completely randomized design is one where subjects are randomly assigned to every combination of treatments in a study d A rigorously controlled study is one where subjects in each treatment comparison group are randomly selected and assigned into the treatment groups and that subjects in the groups as well as those who administer the treatments are not aware (to the extent possible) what the effects of the specific treatments given to a given group are expected to be e Replication relates to repeating a study with different, and perhaps more, subjects to determine if results are consistent or supportive among the studies Cumulative Review Exercises Percentages a 57% of 1500 is 0.57 ∗ 1500= 855 b 26% of 950 is 0.26 ∗ 950= 247 Percentages in a Gallop Poll a 52% of 1038 is 0.52 ∗ 1038= 540 respondents indicated secondhand smoke was “very harmful” b 52 out of 1038 is equal to 52/1038 ∗ 100%= 0.050 ∗ 100%= 5% of the respondents felt secondhand smoke was “not at all harmful” Percentages in a Study of Lipitor a 19 out of 270 is equal to 19/270 ∗ 100%= 0.070 ∗ 100%= 7% of patients who received a reported headaches b 3% of the 270 patients reported back pains, this is 3%/100% ∗ 270= 0.03 ∗ 270= patients out of 270 reported back pains placebo Percentages in Campus Crime Of the 1875 respondents, 8% indicated they had committed a campus crime This would be 0.08 ∗ 1875= 150 respondents Of these 150 respondents, 62% indicated they had done this while under the influence of alcohol or drugs This would be 0.62 ∗ 150= 93 respondents, the number who indicated they had committed a campus crime while under the influence of alcohol or drugs While this is the number who say they have done this, there is no basis for saying that they actually did commit such a crime while under the influence Even though the respondents were anonymous, this is the type of behavior that is likely under-reported since some students would not want to admit either of these actions Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file 6at./ Chapter 1: Introduction Percentages in the Media This would relate to using a ratio scale where zero would represent the absence of plaque For such a scale, the observation of the condition can only be reduced by 100% Once that is done, there is no more to be reduced Phony Data If there are 20 in a group, then the percentages would have to be in units of 1/20 ∗ 100%= 5% Thus, only percentages that are evenly divided by 5% would be valid None of the six percentages presented would be valid In Exercises – 10, the given expressions are designed to yield results expressed in the form of scientific notation Use a calculator or computer to perform the indicated operation and express the result as an ordinary number that is not in scientific notation 0.95500 = 7.2744916E-12= 0.0000000000072744916 (moving the decimal point 12 places to the left) 814= 4.3980465E12= 4,398,046,500,000 (moving the decimal point 12 places to the right) 912= 2.8242954E11= 282,429,540,000 (moving the decimal point 11 places to the right) 10 0.2517= 5.8207661E-11= 0.000000000058207661 (moving the decimal point 11 places to the left) Full file at ... provide a representative sample than has been the case in the past Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file Ch a 12 Diet Stratified,... selected Full file at Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file 4at./ Chapter 1: Introduction 28 Random Selection This would be a randomly selected.. .Solution Manual for Biostatistics for the Biological and Health Sciences by Triola Full file 2at./ Chapter 1: Introduction 18 This would be a sample that is likely not representative of the