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Statistics For The Life Sciences 5th Edition Myra Samuels, Jeffrey Witmer, Andrew Schaffner - Solutions
In a certain population, 83% of the people have Rh-positive blood type.36 Suppose a random sample of n = 10 people is to be chosen from the population and let represent the Wilson-adjusted proportion of Rh-positive people in the sample. Find(a) Pr{= 0.714}(b) Pr{= 0.786}
The appearance of leaf pigment glands in the seedling stage of cotton plants is genetically controlled. According to one theory of the control mechanism, the population ratio of glandular to glandless plants resulting from a certain cross should be 11:5; according to another theory it should be
(a) If the 11:5 and 13:3 ratios are the only two reasonable theories to consider, would you have compelling evidence that the theory you selected in Exercise 9.S.12 is the correct theory? Explain. (b) If there are also other possible theoretical ratios that weren't considered, would you have
When fleeing a predator, the minnow Fundulus notti will often head for shore and jump onto the bank. In a study of spatial orientation in this fish, individuals were caught at various locations and later tested in an artificial pool to see which direction they would choose when released: Would they
Refer to the cortex-weight data of Exercise 8.4.4.(a) Use a goodness-of-fit test to test the hypothesis that the environmental manipulation has no effect. As in Exercise 8.4.4, use a directional alternative and let α = 0.05. (This exercise shows how, by a shift of viewpoint, the sign test can be
A biologist wanted to know if the cowpea weevil has a preference for one type of bean over others as a place to lay eggs. She put equal amounts of four types of seeds into a jar and added adult cowpea weevils. After a few days she observed the following data48:Do these data provide evidence of a
An experiment was conducted in which two types of acorn squash were crossed. According to a genetic model, 1/2 of the resulting plants should have dark stems and dark fruit, 1/4 should have light stems and light fruit, and 1/4 should have light stems and plain fruit. The actual data were 220, 129,
Each of 36 men was asked to touch the backs of the hands of three women, one of whom was the man's romantic partner, while blindfolded. The two "decoy" women were the same age, height, and weight as the man's partner.33 Of the 36 men tested, 16 were able to correctly identify their partner. Do the
In a study of resistance to a certain soybean virus, biologists cross-fertilized two soybean cultivars. They expected to get a 3:1 ratio of resistant to susceptible plants. The observed data were 58 resistant and 26 susceptible plants.50 Are these data significantly inconsistent with the expected
In a population of flatworms (Planaria) living in a certain pond, one in five individuals is adult and four are juvenile.37 An ecologist plans to count the adults in a random sample of 16 flatworms from the pond; she will then use P, the Wilson-adjusted sample proportion of adults in the sample, as
A group of 1,438 sexually active patients were counseled on condom use and the risk of contracting a sexually transmitted disease (STD). After 6 months, 103 of the patients had new STDs.51 Construct a 95% confidence interval for the probability of contracting an STD within 6 months after being part
Suppose that for (uncounseled) sexually active individuals the probability of acquiring an STD in a 6-month period is 10%.(a) Using your interval computed in Exercise 9.S.21, is there compelling evidence that the 6-month STD probability is different for those who receive counseling?(b) Using the
Refer to Exercise 9.S.3. Which of the conditions for validity of the confidence interval might have been violated in this study?Exercise 9.S.39.5.3In a study of environmental effects upon reproduction. 123 female adult white-tailed deer from the central Adirondack area were captured, and 97 were
A sample of 32 breastfed infants found that 2 of them developed iron deficiency by age 5.5 months.39 (a) Use these data to construct an appropriate 90% confidence interval. (b) What conditions are necessary for the confidence interval from part (a) to be valid? (c) Interpret your confidence
A certain California winery produces 720,000 bottles of wine each year. Suppose you want to estimate the proportion of those bottles that have cork taint (i.e., the wine is spoiled due to a failure of the cork). Suppose that 4% of all corked wine has cork taint. Using this as a pre-liminary guess
Refer to Exercise 9.S.6. Suppose you do not trust that the 4% taint rate for wines in general is a useful guess for this particular winery. (a) Suppose that, based on previous years of data at this winery, about 10% of the wines have had cork taint. How many bottles would need to be included in a
When male mice are grouped, one of them usually becomes dominant over the others. In order to see how a parasitic infection might affect the competition for dominance, male mice were housed in groups, three mice to a cage; two mice in each cage received a mild dose of the parasitic worm H.
Are mice right-handed or left-handed? In a study of this question, 320 mice of a highly inbred strain were tested for paw preference by observing which forepaw-right or left -they used to retrieve food from a narrow tube. Each animal was tested 50 times, for a total of 320 × 50 =
The accompanying partially complete contingency table shows the responses to two treatments:(a) Invent a fictitious data set that agrees with the table and for which x2s = 0.(b) Calculate the estimated probabilities of success r{Success | Treatment 1} and r {Success | Treatment 2} for your data
In a randomized clinical trial to determine the most effective timing of administration of chemotherapeutic drugs to lung cancer patients, 16 patients were given four drugs simultaneously and 11 patients were given the same drugs sequentially. Objective response to the treatment (defined as
Physicians conducted an experiment to investigate the effectiveness of external hip protectors in pre-venting hip fractures in elderly people. They randomly assigned some people to get hip protectors and others to be the control group. They recorded the number of hip fractures in each group. Do the
A sample of 276 healthy adult volunteers were asked about the variety of social networks that they were in (e.g., relationships with parents, close neighbors, workmates, etc.).They were then given nasal drops containing a rhinovirus and were quarantined for 5 days. Of the 123 subjects who were in
The drug ancrod was tested in a double-blind clinical trial in which subjects who had strokes were randomly assigned to get either ancrod or a placebo. One response variable in the study was whether or not a subject experienced intracranial hemorrhaging. The data are provided in the following
Do women respond to men's solicitations more readily during the fertile phase of their menstrual cycles? In a study of this question, each of two hundred 18- to 25-year-old women who were walking alone in a city were approached by an attractive 20-year-old man who solicited the woman's telephone
To compare the impacts of roads in two adjacent ecoregions in Brazil researchers sampled stretches of roadway over a period of 7 years in each region and recorded the species of animals killed by vehicles. In the-Atlantic Forest habitat there were 178 roadkills observed, of which 51 were six-banded
Proceed as in Exercise 10.2.1 for the following contingency table:Exercise 10.2.1The accompanying partially complete contingency table shows the responses to two treatments:(a) Invent a fictitious data set that agrees with the table and for which x2s = 0.(b) Calculate the estimated probabilities of
Proceed as in Exercise 10.2.1 for the following contingency table:Exercise 10.2.1The accompanying partially complete contingency table shows the responses to two treatments:(a) Invent a fictitious data set that agrees with the table and for which x2s = 0.(b) Calculate the estimated probabilities of
Most salamanders of the species P.cinereus are red striped, but some individuals are all red. The all-red form is thought to be a mimic of the salamander N.viridescens, which is toxic to birds. In order to test whether the mimic form actually survives more successfully, 163 striped and 41 red
Can attack of a plant by one organism induce resistance to subsequent attack by a different organism? In a study of this question, individually potted cotton (Gossypium) plants were randomly allocated to two groups. Each plant in one group received an infestation of spider mites (Tetranychus); the
It has been suspected that prolonged use of a cellular telephone increases the chance of developing brain cancer due to the microwave-frequency signal that is transmitted by the cell phone. According to this theory, if a cell phone is repeatedly held near one side of the head, then brain tumors are
Phenytoin is a standard anticonvulsant drug that unfortunately has many toxic side effects. A study was undertaken to compare phenytoin with valproate, another drug in the treatment of epilepsy. Patients were randomly allocated to receive either phenytoin or valproate for 12 months. Of 20 patients
Estrus synchronization products are used to bring cows into heat at a predictable time so that they can be reliably impregnated by artificial insemination. In a study of two estrus synchronization products, 42 mature cows (ages 4-8 years) were randomly allocated to receive either product A or
Experimental studies of cancer often use strains of animals that have a naturally high incidence of tumors. In one such experiment, tumor-prone mice were kept in a sterile environment; one group of mice was maintained entirely germ free, while another group was exposed to the intestinal bacterium
Consider a fictitious population of mice. Each animal's coat is either black (B) or gray (G) in color and is either wavy (W) or smooth (S) in texture. Express each of the following relationships in terms of probabilities or conditional probabilities relating to the population of animals. (a) Smooth
A randomized experiment was conducted in which patients with coronary artery disease either had angioplasty or bypass surgery. The accompanying table shows the incidence of angina (chest pain) among the patients 5 years after treatment.Let A represent angioplasty and B represent bypass. (a)
Refer to Exercise 10.3.10. Invent a fictitious data set on coronary treatment and angina for 1,000 patients, for which r{Yes | A} is twice as great as r{ Yes | B}, but nevertheless the majority of patients who have angina also had bypass surgery (as opposed to angioplasty).Exercise 10.3.10A
Suppose pairs of fraternal twins are examined and the handedness of each twin is determined: assume that all the twins are brother-sister pairs. Suppose data are collected for 1,000 twin pairs, with the results shown in the following table. State whether each of the following statements is true or
Consider a fictitious population of mice in which each animal's coat is either black (B) or gray (G) in color and is either wavy (W) or smooth (S) in texture (as in Exercise 10.3.1). Suppose a random sample of mice is selected from the population and the coat color and texture are observed;
Men with prostate cancer were randomly assigned to undergo surgery (n = 347) or "watchful waiting" (no surgery, n = 348). Over the next several years there were 83 deaths in the first group and 106 deaths in the second group. The results are given in the table.(a) Let D and A represent died and
In a study of behavioral asymmetries, 2,391 women were asked which hand they preferred to use (e.g., to write) and which foot they preferred to use (for instance, to kick a ball). The results are reported in the table.(a) Estimate the conditional probability that a woman is right-footed, given that
Consider a study to investigate a certain suspected disease-causing agent. One thousand people are to be chosen at random from the population; each individual is to be classified as diseased or not diseased and as exposed or not exposed to the agent. The results are to be cast in the following
Refer to Exercise 10.3.5. Invent fictitious data sets as specified, and verify your answer by calculating appropriate estimated conditional probabilities. (Your data need not be statistically significant.)(a) Invent a data set for whichr{DY | EY} > r{DY | EN} butr{EY | DY} r{EN | DY}or explain why
An ecologist studied the spatial distribution of tree species in a wooded area. From a total area of 21 acres, he randomly selected 144 quadrats (plots), each 38 feet square, and noted the presence or absence of maples and hickories in each quadrat. The results are shown in the table.The value of
Refer to Exercise 10.3.8. Suppose the data for fictitious tree species, A and B, were as presented in the accompanying table. The value of the chi-square statistic for this contingency table is χ2s = 9.07. As in Exercise 10.3.8, test the null hypothesis of independence and interpret your
Consider conducting Fisher's exact test with the following fictitious table of data. Let the null hypothesis be that treatment and response are independent, and let the alternative be the directional hypothesis that treatment B is better than treatment A. List the tables of possible outcomes that
Repeat Exercise 10.4.1 with the following table of data.Exercise 10.4.1 Consider conducting Fisher's exact test with the following fictitious table of data. Let the null hypothesis be that treatment and response are independent, and let the alternative be the directional hypothesis that treatment B
A randomized trial of clinically obese women examined the efficacy and safely of a partial meal replacement diet using nutritionally fortified meal-replacement shakes. Fourteen clinically obese women received the nutritional shakes and healthy diet counseling during their pregnancy. Another nine
A random sample of 99 students in a Conservatory of Music found that 9 of the 48 women sampled had "perfect pitch" (the ability to identify, without error, the pitch of a musical note), but only 1 of the 51 men sampled had perfect pitch. Conduct Fisher's exact test of the null hypothesis that
Consider the data from Exercise 10.4.5. Conduct a chi-square test and compare the results of the chi-square test to the results of Fisher's exact test. Exercise 10.4.5 A random sample of 99 students in a Conservatory of Music found that 9 of the 48 women sampled had "perfect pitch" (the ability to
The growth factor pleiotrophin is associated with cancer progression in humans. In an attempt to monitor the growth of tumors, doctors measured serum pleiotrophin levels in patients with pancreatic cancer and in a control group of patients. They found that only 2 of 28 control patients had serum
A group of 225 men with benign prostatic hyperplasia were randomly assigned to take saw palmetto extract or a placebo in a double-blind trial. One year into the experiment 45 of the 112 men in the saw palmetto group (40%) thought they were taking saw palmetto, compared to 52 of the 113 men in the
An experiment involving subjects with schizophrenia compared "personal therapy" to "family therapy." Only 2 out of 23 subjects assigned to the personal therapy group suffered psychotic relapses in the first year of the study, compared to 8 of the 24 subjects assigned to the family therapy group. Is
Patients with painful knee osteoarthritis were randomly assigned in a clinical trial to one of five treatments: glucosamine, chondroitin, both, placebo, or Celebrex, the standard therapy. One outcome recorded was whether or not each patient experienced substantial improvement in pain or in ability
Is acupuncture effective on back pain? Patients with chronic low back pain were randomly assigned to one of four groups. Some patients received standardized acupuncture, while others received acupuncture that was individualized. A third group was given simulated acupuncture in which a toothpick was
Consider the data from Exercise 10.5.10. Suppose the Usual Care group is excluded and comparison is made only between the first three treatments: the two types of real acupuncture and the simulated acupuncture. Here is computer output for a chi-square test to compare the three groups.X-squared =
For a study of free-living populations of the fruitfly Drosophila subobscura, researchers placed baited traps in two woodland sites and one open-ground area. The numbers of male and female flies trapped in a single day are given in the table.Here is computer output for a chi-square test to compare
In a classic study of peptic ulcer, blood types were determined for 1,655 ulcer patients. The accompanying table shows the data for these patients and for an independently chosen group of 10.000 healthy controls from the same city.(a) The value of the chi-square statistic for this contingency table
The two claws of the lobster (Homarus americanus) are identical in the juvenile stages. By adulthood, however, the two claws normally have differentiated into a stout claw called a "crusher" and a slender claw called a "cutter." In a study of the differentiation process, 26 juvenile lobsters were
A randomized, double-blind, placebo-controlled experiment was conducted in which patients with Alzheimer's disease were given either extract of Ginkgo biloba (EGb) or a placebo for one year. The change in each patient's Alzheimer's Disease Assessment Scale - Cognitive subscale (ADAS-Cog) score was
Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of the year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protoiluua staminea. She collected a sample of 78 clam shells
A group of patients with a binge-eating disorder were randomly assigned to take either the experimental drug fluvoxamine or a placebo in a 9-week long double-blind clinical trial. At the end of the trial the condition of each patient was classified into one of four categories: no response, moderate
Patients with coronary artery disease were randomly assigned to either receive angioplasty plus medical therapy (n = 1149) or medical therapy alone (n = 1138) in a clinical trial. Over the next several years 85 angioplasty and 95 medical therapy patients died, with cause of death categorized as
Patients with pleural infections (fluid buildup in the chest) were randomly assigned to placebo, the treatment "tPA" (tissue plasminogen activator), the treatment "DNase" (deoxyribonuclease),or a combination of tPA and DNase in a double-blind clinical trial. Some of the patients needed to be given
In a study of prenatal influences on susceptibility to seizures in mice, pregnant females were randomly allocated to a control group or a "handled" group. Handled mice were given sham injections three times during gestation, while control mice were not touched. The offspring were tested for their
In control of diabetes it is important to know how blood glucose levels change after eating various foods. Ten volunteers participated in a study to compare the effects of two foods -a sugar and a starch. A blood specimen was drawn before each volunteer consumed a measured amount of food: then
Elderly patients who had suffered hip fractures were randomly assigned to receive either a placebo (n = 1,062) or zolendronic acid (n = 1,065) in a double-blind clinical trial. During the trial 139 placebo patients and 92 zolendronic acid patients had new fractures. Let p1 and p2 represent the
Refer to the liver tumor data of Exercise 10.2.9.(a) Construct a 95% confidence interval for (Pr{liver tumor | germ-free} - Pr{liver tumor | E. coli}).(b) Interpret the confidence interval from part (a). That is. explain what the interval tells you about tumor probabilities.Exercise
For women who are pregnant with twins, complete bed rest in late pregnancy is commonly prescribed in order to reduce the risk of premature delivery. To test the value of this practice, 212 women with twin pregnancies were randomly allocated to a bed-rest group or a control group. The accompanying
Refer to the blood type data of Exercise 10.5.3. Let p1 and p2 represent the probabilities of type O blood in the patient population and the control population, respectively.(a) Construct a 95% confidence interval for (p1 - p2).(b) Interpret the confidence interval from part (a). That is, explain
In an experiment to treat patients with "generalized anxiety disorder," the drug hydroxyzine was given to 71 patients, and 30 of them improved. A group of 70 patients were given a placebo, and 20 of them improved. Let p1 and p2 represent the probabilities of improvement using hydroxyzine and the
As part of a study of risk factors for stroke, 155 women who had experienced a hemorrhagic stroke (eases) were interviewed. For each case, a control was chosen who had not experienced a stroke; the control was matched to the case by neighborhood of residence, age, and race. Each woman was asked
Example 10.S.1 referred to a sample of HIV-infected women who gave birth to two children. One of the outcomes that was studied was whether the gestational age of the child was less than 38 weeks; this information was recorded for 106 of the families. The data lor this variable are shown in the
A study of 85 patients with Hodgkin's disease found that 41 had had their tonsils removed. Each patient w as matched with a sibling of the same sex. Only 33 of the siblings had undergone tonsillectomy. The data are shown in the following tabled Use McNemar's test to test the hypothesis that
In a study of the mating behavior of Gryllus campestris, pairs of female crickets were placed in a plexiglass arena with a single male cricket. There were 54 cases in which the females fought; these resulted in 42 cases in which the winning female copulated with the male, 8 cases in which the
For each of the following tables, calculate (i) the relative risk and (ii) the odds ratio.(a)(b)
For each of the following tables, calculate (i) the relative risk and (ii) the odds ratio.(a)(b)
Hip dysplasia is a hip socket abnormality that affects many large breed dogs. A review of medical records of dogs seen at 27 veterinary medical teaching hospitals found that hip dysplasia was more common in Golden Retrievers than in Border Collies; the data are shown in the following table.
Consider the data from Exercise 10.9.3.(a) Calculate the sample value of the odds ratio.(b) Construct a 95% confidence interval for the population value of the odds ratio.(c) Interpret the confidence interval from part (b) in the context of this setting.Exercise 10.9.3
As part of the National Health Interview Survey, occupational injury data were collected on thousands of American workers. The table below summarizes part of these data.(a) Calculate the sample value of the odds ratio.(b) According to the odds ratio, are self-employed workers more likely, or less
Many over-the-counter decongestants and appetite suppressants contain the ingredient phenylpropanol-amine. A study was conducted to investigate whether this ingredient is associated with strokes. The study found that 6 of 702 stroke victims had used an appetite suppressant containing
Two treatments, heparin and enoxaparin, were compared in a double-blind, randomized clinical trial of patients with coronary artery disease. The subjects can be classified as having a positive or negative response to treatment; the data are given in the following table.(a) Calculate the sample
Consider the data from Exercise 10.7.1. Given that there were 139 hip fractures in 1.062 placebo patients and 92 hip fractures in 1,065 zolendronic acid patients, construct a 95% confidence interval for the population value of the odds ratio.Exercise 10.7.1Two treatments, heparin and enoxaparin,
Researchers in Norway found that of 61,042 children born to women who took folic acid while pregnant there were 64 who developed autism. This compares to 50 out of 24,134 for women who did not take folic acid. (a) Calculate the sample value of the odds ratio. (b) Construct a 95% confidence interval
In the Women's Health Initiative Dietary Modification Trial women were randomly assigned to an intervention or a control group. The intervention included counseling sessions designed to reduce fat intake and to increase consumption of fruits and vegetables. Over 6 years data were collected on
Two drugs, zidovudine and didanosine, were tested for their effectiveness in preventing progression of HIV disease in children. In a double-blind clinical trial, 276 children with HIV were given zidovudine, 281 were given didanosine, and 274 were given zidovudine plus didanosine. The following
The blood types of malaria patients at a clinic in India were compared with those obtained in a sample of visitors to a nearby hospital. The data are shown in the following table. Use these data to conduct a test of the null hypothesis that blood type is independent of contracting malaria.Here is
The habitat selection behavior of the fruitfly Drosophila subobscura was studied by capturing flies from two different habitat sites. The flies were marked with colored fluorescent dust to indicate the site of capture and then released at a point midway between the original sites. On the following
In the garden pea Pisum sativum, seed color can be yellow (Y) or green (G), and seed shape can be round (R) or wrinkled (W). Consider the following three hypotheses describing a population of plants:H(1)0: Pr{Y} = 3/4H(2)0: Pr{R} = 3/4H(3)0: Pr{Y} = Pr{R | G}The first hypothesis asserts that yellow
A study of 36,080 persons who had heart attacks found that men were more likely to survive than were women. The following table shows some of the data collected in the study.(a) Calculate the odds ratio for comparing survival of men to survival of women. (b) Calculate a 95 % confidence interval for
In the study described in Exercise 10.9.6, one of the variables measured was whether the subjects had used any products containing phenylpropanolamine. The odds ratio was calculated to be 1.49, with stroke victims more likely than the control subjects to have used a product containing
In a study of the effects of smoking cigarettes during pregnancy, researchers examined the placenta from each of 58 women after childbirth. They noted the presence or absence (P or A) of a particular placental abnormality -atrophied villi. In addition, each woman was categorized as a non-smoker
Prior to an influenza season subjects were randomly assigned to receive either a flu vaccine or a placebo. During thatseason there were 28 cases of the flu among 813 vaccine recipients and 35 cases of the flu among the 325 subjects who were given the placebo.76 Do these data indicate that the
Refer to the data in Exercise 10.S.18.(a) Calculate the sample odds ratio.(b) Find a 95% confidence interval for the population value of the odds ratio.Exercise 10.S.18
Use the data from Exercise 10.S.1 to construct a 95% confidence interval for (Pr{CHD | intervention} -Pr{CHD | control}).Exercise 10.S.1
Consider Exercise 9.S.18. The romantic partners of the 36 men discussed in Exercise 9.S.18 were also tested, in the same manner as the men (i.e., they were blindfolded and asked to identify their partner by touching the backs of the hands of three men, one of whom was their partner). Among the
A researcher found that 54 out of 66 randomly selected trees in an arboretum in northern Ohio were native species. This compared to 42 out of 72 randomly chosen trees in "managed" land in the same general area. Is there significant evidence of a difference in proportions? If so, how strong is that
As part of a study of environmental influences on sex determination in the fish Menidia, eggs from a single mating were divided into two groups and raised in either a warm or a cold environment. It was found that 73 of 141 offspring in the warm environment and 107 of 169 offspring in the cold
A group of mountain climbers participated in a trial to investigate the usefulness of the drug acetazolamide in preventing altitude sickness. The climbers were randomly assigned to receive either drug or placebo during an ascent of Mt. Rainier. The experiment was sup-posed to be double-blind, but
Desert lizards (Dipsosaurus dorsalis) regulate their body temperature by basking in the sun or moving into the shade, as required. Normally the lizards will maintain a daytime temperature of about 38°C. When they are sick, however, they maintain a temperature about 2o to 4o higher -that is, a
Consider the data from Exercise 10.S.6. Analyze these data with a chi-square test. Let α = 0.05.Exercise 10.S.6Desert lizards (Dipsosaurus dorsalis) regulate their body temperature by basking in the sun or moving into the shade, as required. Normally the lizards will maintain a daytime
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