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statistics

Questions and Answers of Statistics

An ecological researcher studied the interaction between birds of two subspecies, the Carolina Junco and the Northern Junco. He placed a Carolina male and a Northern male, matched by size, together
(a) Suppose a paired data set has nD = 4 and Bs = 4. Calculate the exact P-value of the data as analyzed by the sign test (against a non directional alternative). (b) Explain why, in Table 7 with nD
The study described in Example 8.1.1, involving the compound mCPP, included a group of men. The men were asked to rate how hungry they were at the end of each 2-week period and differences were
Use Table 8 to find the P-value for a Wilcoxon signed-rank test (against a nondirectional alternative), assuming that nD = 7 and (a) Ws = 22 (b) Ws = 25 (c) Ws = 26 (d) Ws = 28
Use Table 8 to find the P-value for a Wilcoxon signed-rank test (against a nondirectional alternative), assuming that nD = 12 and (a) Ws = 55 (b) Ws = 65 (c) Ws = 71 (d) Ws = 73
The study described in Example 8.1.1, involving the compound mCPP, included a group of nine men. The men were asked to rate how hungry they were at the end of each 2-week period and differences were
As part of the study described in Example 8.1.1(and in Exercise 8.5.3), involving the compound mCPP, weight change was measured for nine men. For each man two measurements were made: weight change
Consider the skin graft data of Example 8.4.1. Table 8.5.5, at the end of Section 8.5, shows the first steps in conducting a Wilcoxon signed-rank test of the null hypothesis that HL-A compatibility
In an investigation of possible brain damage due to alcoholism, an X-ray procedure known as a computerized tomography (CT) scan was used to measure brain densities in 11 chronic alcoholics. For each
In a study, on the effect of caffeine on myocardial blood flow, 10 subjects had their blood flow measured before and after consuming caffeine.21 For this setting the differences do not follow a
Thirty-three men with high serum cholesterol, all regular coffee drinkers, participated in a study to see whether abstaining from coffee would affect their cholesterol level. Twenty-five of the men
Eight young women participated in a study to investigate the relationship between the menstrual cycle and food intake. Dietary information was obtained every day by interview; the study was
For each of 29 healthy dogs, a veterinarian measured the glucose concentration in the anterior chamber of the left eye and the right eye, with the results shown in the table.Using the paired /
Tobramycin is a powerful antibiotic. To minimize its toxic side effects, the dose can be individualized for each patient. Thirty patients participated in a study of the accuracy of this
Can keeping cows out of a creek on ranchland improve the water quality? To answer this question environmental researchers measured the coliform on grazed ranch land. Then, a fence was installed along
A volunteer working at an animal shelter conducted a study of the effect of catnip on cats at the shelter. She recorded the number of "negative interactions" each of 15 cats made in 15-minute periods
Refer to Exercise 8.S.6. Analyze these data using a Wilcoxon signed-rank test.Exercise 8.S.6.Biologists noticed that some stream fishes are most often found in pools, which are deep, slow-moving
In a study of the effect of caffeine on muscle metabolism, nine male volunteers underwent arm exercise tests on two separate occasions. On one occasion, the volunteer took a placebo capsule an hour
For the data of Exercise 8.S.12, construct a display like that of figure 8.1.1Exercise 8.S.12In a study of the effect of caffeine on muscle metabolism, nine male volunteers underwent arm exercise
Refer to Exercise 8.S.12. Analyze these data using a sign test.Exercise 8.S.12In a study of the effect of caffeine on muscle metabolism, nine male volunteers underwent arm exercise tests on two
Certain types of nerve cells have the ability to regenerate a part of the cell that has been amputated. In an early study of this process, measurements were made on the nerves in the spinal cord in
Aldosterone is a hormone involved in maintaining fluid balance in the body. In a veterinary study, six dogs with heart failure were treated with the drug Captopril, and plasma concentrations of
Refer to Exercise 8.S.16. Analyze these data using a Wilcoxon signed - rank test.Exercise 8.S.16Aldosterone is a hormone involved in maintaining fluid balance in the body. In a veterinary study, six
Refer to Exercise 8.S.16. Note that the dogs in this study are not compared to a control group. How does this weaken any inference that might be made about the effectiveness of Captopril?
For an investigation of the mechanism of wound healing, a biologist chose a paired design, using the left and right hindlimbs of the salamander Notophthalmus viridescens. After amputating each limb,
In a study of hypnotic suggestion, 16 male volunteers were randomly allocated to an experimental group and a control group. Each subject participated in a two-phase experimental session. In the first
Suppose we want to test whether an experimental drug reduces blood pressure more than does a placebo. We are planning to administer the drug or the placebo to some subjects and record how much their
A group of 20 postmenopausal women were given transdermal estradiol for one month. Plasma levels of plasminogen-activator inhibitor type 1 (PAI-1) went down for 10 of the women and went up for the
Six patients with renal disease underwent plasmapheresis. Urinary protein excretion (grams of protein per gram of creatinine) was measured for each patient before and after plasmapheresis. The data
Refer to Exercise 8.S.I. Compare the before and after populations using a sign test at Î± = 0.05. Use a non directional alternative.Exercise 8.S.I.A volunteer working at an animal
Refer to Exercise 8.S.I. Construct a scatterplot of the data. Does the appearance of the scatterplot indicate that the pairing was effective? Explain.Exercise 8.S.I.A volunteer working at an animal
As part of a study of the physiology of wheat maturation, an agronomist selected six wheat plants at random from a field plot. For each plant, she measured the moisture content in two batches of
Biologists noticed that some stream fishes are most often found in pools, which are deep, slow-moving parts of the stream, while others prefer riffles, which are shallow, fast-moving regions. To
Refer to Exercise 8.S.6. What conditions are necessary for the confidence interval to be valid? Are those conditions satisfied? How do you know?Exercise 8.S.6Biologists noticed that some stream
Refer to Exercise 8.S.6. Compare the habitats using a t test at Î± = 0.10. Use a non directional alternative.Exercise 8.S.6Biologists noticed that some stream fishes are most often found
Refer to Exercise 8.S.6.(a) Compare the habitats using a sign test at Î± = 0.10. Use a non directional alternative.(b) Use the binomial formula to calculate the exact P-value for part
Let Y denote the fruit weight of a nectarine. Suppose Nancy wants to know how weights in her orchard com-pared from this season to the last. In particular, suppose she is interested in the averages
Consider studying whether drug A and drug B are equally effective in lowering blood pressure. For each of (a), (b), and (c) answer two questions (you do not need to explain your answers):(I) What
Fred collects data from two populations. Maria uses those data to construct a (two-sided) 90% confidence interval for μ1, - μ2, and gets (-3.4,23.7). At the same time Sam uses the data to test H0:
[Based on Koh, et al. (1997). Effects of hormone-replacement therapy on fibrinolysis in postmenopausal women. New England Journal of Medicine 336,683-690, which is the basis of Exercise 8.S.22.]
A random sample of 50 subjects received biofeedback training to reduce blood pressure. Researchers measured the decrease in blood pressure for each of them; the average decrease was 11.4, and the SD
Suppose we want to test whether an experimental drug reduces blood pressure more than does a placebo. We are planning to administer the drug or placebo to some subjects and record how much their
Consider the research question: Can training reduce stress in cats when they are getting their blood drawn? (a) In plain English, write the null and alternative hypotheses of interest to the
Below are histograms and normal probability plots and Shapiro-Wilk test F-values of the Cortisol levels of the 31 cats in the study.Shapiro - wilk p - value = 0.0001 Shapiro - wilk p - value =
For each of the following statements say whether they are true or false and explain why.(a) If training is truly unrelated to stress (Cortisol) levels, a larger study would have more power than a
The researchers also measured the number of escape attempts during the medical procedure for each cat. A 95% confidence interval for the difference in mean number of escape attempts (per cat) was
Each of 41 students at a college was asked to calculate their "ecological footprint" -the number of hectares required to support their existence, taking into account such things as the land needed to
As part of a study to determine the effect of flaxseed on blood thiocyanate concentration in rats, the authors reported the amount of hydrogen cyanide (HCN) in the flaxseed fed to the rats. This
For each of the following research studies, identify whether independent samples (e.g., two-sample t test, Wilcoxon-Mann-Whitney) or paired samples (e.g., paired t test, sign test) would most likely
Consider the study described in 11.21(b). (a) Considering conducting a study of the same size to answer the same question as described in 11.21(b), describe in detail a study design that would use
After seeing the sample means and SDs from Question II.2, Norman became concerned that a t lest might not be appropriate here, so he wants Rebecca to do a different analysis. (a) Why is Norman
Suppose someone constructs a 95% confidence interval for μ1 - μ2 and gets (1.3,12.7). If we were to test H0: μ1 = μ2 versus HA: μ1 ≠ μ2 with a = 0.10, would we reject H0? Or can we not tell
Nitric oxide is sometimes given to newborns who experience respiratory failure. In one experiment, nitric oxide was given to 114 infants. This group was compared to a control group of 121 infants.
Researchers took random samples of subjects from two populations and applied a two-sample t test to the data using α = 0.10: the P-value for the test, using a nondirectional alternative, was 0.06.
Researchers measured blood levels of the hormone Androstenedione (Andro) in each of 24 women. Among 12 women who had recently fallen in love, the sample mean was 2.1 ng/ml; the SD of these data was
Consider the process of planning for adequate power when designing an experiment for which a two-sample t test will be used.(a) Suppose the effect size is constant and the chosen alpha level is also
A researcher did a randomization test to compare men and women on a variable Y. The null hypothesis is that men and women are the same, and the alternative is that they are different. There are 28
Consider taking a random sample of size 3 from a population of persons who smoke and recording how many of them, if any, have lung cancer. Let represent the Wilson-adjusted proportion of persons in
Consider taking a random sample of size 10 from the population of students at a certain college and asking each of the 10 students whether or not they smoke. In the context of this setting, explain
Suppose we are to draw a random sample of three individuals from a large population in which 37% of the individuals are mutants (as in Example 3.6.4). Let represent the Wilson-adjusted proportion of
Suppose we are to draw a random sample of five indi-viduals from a large population in which 37% of the indi-viduals are mutants (as in Example 3.6.4). Let represent the Wilson-adjusted proportion
A new treatment for acquired immune deficiency syndrome (AIDS) is to be tested in a small clinical trial on 15 patients. The Wilson-adjusted proportion P who respond to the treatment will be used as
In a certain forest, 25% of the white pine trees are infected with blister rust. Suppose a random sample of four white pine trees is to be chosen, and let be the Wilson-adjusted sample proportion of
(a) Determine the sampling distribution of for samples of size n = 8 white pine trees from the same forest.(b) Construct graphs of the sampling distributions of for n = 4 and for n = 8, using the
The shell of the land snail Limocolaria marfensiana has two possible color forms: streaked and pallid. In a certain population of these snails. 60% of the individuals have streaked shells (as in
In a certain community. 17% of the soda dispensers are contaminated (as in Example 9.1.3). Suppose a random sample of five dispensers is to be chosen and the contamination observed. Let represent
Consider random sampling from a dichotomous population: let E be the event that is within ±0.05 of p. In Example 9.1.5, we found that Pr{E} = 0.53 for n = 20 and p = 0.17. Calculate Pr{E} for n =
A series of patients with bacterial wound infections were treated with the antibiotic Cefotaxime. Bacteriologic response (disappearance of the bacteria from the wound) was considered "satisfactory"
Refer to Exercise 9.2.9. Suppose a study is being planned for a part of the world for which the percentage of tasters is completely unknown, so the 70% figure used in Exercise 9.2.9 is not
The "Luso" variety of wheat is resistant to the Hessian fly. In order to understand the genetic mechanism controlling this resistance, an agronomist plans to examine the progeny of a certain cross
Suppose the agronomist is considering two possible genetic mechanisms for the inheritance of resistance; the population ratio of resistant to susceptible progeny would be 1:1 under one mechanism and
In a study of in vitro fertilization, 264 women ages 40-44 underwent a procedure known as elective single-embryo transfer (cSET) to attempt to get pregnant. Sixty of these women successfully became
Consider the data from Exercise 9.2.14. Suppose a new study of the effectiveness of eSET is being considered for women ages 35-39, and it is desired to have a standard error no greater than 0.04. How
A researcher found that 54 out of 66 trees sampled in an arboretum were native species to the area. Using these data, he calculated a 95% confidence interval as (0.71,0.89).15 (a) The confidence
In a study of hand hygiene compliance in hospital surgical wards, researchers observed 375 instances for which hand washing would have been appropriate. Among the 375 observations, hands were washed
In an experiment with a certain mutation in the fruitfly Drosophila, n individuals were examined; of these, 20% were found to be mutants. Determine the standard error of if (a) n = 100 (20
Refer to Exercise 9.2.2. In each case (n = 100 and n = 400) construct a 95% confidence interval for the population proportion of mutants.Exercise 9.2.2In an experiment with a certain mutation in the
In a natural population of mice (Mas musculus) near Ann Arbor, Michigan, the coats of some individuals are white spotted on the belly. In a sample of 580 mice from the population, 28 individuals were
To evaluate the policy of routine vaccination of infants for whooping cough, adverse reactions were monitored in 339 infants who received their first injection of vaccine. Reactions were noted in 69
In a study of human blood types in nonhuman primates, a sample of 71 orangutans were tested, and 14 were found to be blood type B. Construct a 95% confidence interval for the relative frequency of
In populations of the snail Cepaea, the shells of sonic individuals have dark bands, while other individuals have unhanded shells." Suppose that a biologist is planning a study to estimate the
What would the answer be if the anticipated percentage of banded snails were 50% rather than 60%?
The ability to taste the compound phenylthiocarbamide (PTC) is a genetically controlled trait in humans. In Europe and Asia, about 70% of people are "tasters."12 Suppose a study is being planned to
In a sample of 848 children ages 3 to 5 it was found that 3.7% of them had iron deficiency.17 Use these data to construct a 90% confidence interval for the proportion of all 3- to 5-year-old children
Researchers tested patients with cardiac pacemakers to see if use of a cellular telephone interferes with the operation of the pacemaker. There were 959 tests conducted for one type of cellular
Gene mutations have been found in patients with muscular dystrophy. In one study, it was found that there were defects in the gene coding of sarcoglycan proteins in 23 of 180 patients with
In an ecological study of the Carolina Junco, 53 birds were captured from a certain population; of these, 40 were male.20 Use these data to construct a 90% confidence interval for the proportion of
A cross between white and yellow summer squash gave progeny of the following colors24:Are these data consistent with the 12:3:1 ratio predicted by a certain genetic model? Use a chi-square test at
Scientists have used Mongolian gerbils when con- ducting neurological research. A certain breed of these gerbils were crossed and gave progeny of the following colors32:(a) What is the value of the
Each of 36 men was asked to touch the foreheads of three women, one of whom was their romantic partner, while blindfolded. The two "decoy" women were the same age, height, and weight as the man's
Geneticists studying the inheritance pattern of cowpea plants classified the plants in one experiment according to the nature of their leaves. The data follow4:Test the null hypothesis that the three
In the snapdragon (Antirrhinum ma jus), individual plants can be red flowered, pink flowered, or white flowered. According to a certain Mendelian genetic model, self-pollination of pink-flowered
Refer to Exercise 9.4.1. Suppose the sample had the same composition but was 10 times as large: 1.550 white, 400 yellow, and 100 green progeny. Would the data be consistent with the 12:3:1 model?
How do bees recognize flowers? As part of a study of this question, researchers used the following two artificial "flowers''25:
At a Midwestern hospital there were a total of 932 births in 20 consecutive weeks. Of these births, 216 occurred on weekends.26 Do these data reveal more than chance deviation from random timing of
In a breeding experiment, white chickens with small combs were mated and produced 190 offspring of the types shown in the accompanying table.27 Are these data consistent with the Mendelian expected
Among n babies born in a certain city, 51% were boys.28 Suppose we want to test the hypothesis that thetrue probability of a boy is 1/2. Calculate the value of x2s, and bracket the P-value for
In an agronomy experiment, peanuts with shriveled seeds were crossed with normal peanuts. The genetic model that the agronomists were considering predicted that the ratio of normal to shriveled
An experimental design using litter-matching was employed to test a certain drug for cancer-causing potential. From each of 50 litters of rats, three females were selected; one of these three, chosen
A study of color vision in squirrels used an apparatus containing three small translucent panels that could be separately illuminated. The animals were trained to choose, by pressing a lever, the

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