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Statistics For The Life Sciences 5th Edition Myra Samuels, Jeffrey Witmer, Andrew Schaffner - Solutions

Human beta-endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. A researcher conducted a study to investigate whether a program of regular exercise might affect the resting (unstressed) concentration of HBE in the blood. He measured blood HBE levels, in January
Consider the data from Exercise 6.3.11. If the sample size is small, as it is in this case, then in order for a confidence interval based on Student's t distribution to be valid, the data must come from a normally distributed population. Is it reasonable to think that difference in HBE level is
Invertase is an enzyme that may aid in spore germination of the fungus Colletotrichum graminicola. A botanist incubated specimens of the fungal tissue in petri dishes and then assayed the tissue for invertase activity. The specific activity values for nine petri dishes incubated at 90% relative
In a study of larval development in the tufted apple budmoth (Platynota idatusalis), an entomologist measured the head widths of 50 larvae. All 50 larvae had been reared under identical conditions and had moulted six times. The mean head width was 1.20 mm and the standard deviation was 0.14 mm.
In a study of the effect of aluminum intake on the mental development of infants, a group of 92 infants who had been born prematurely were given a special aluminum-depleted intravenous-feeding solution.18 At age 18 months the neurologic development of the infants was measured using the Bayley
In Exercise 6.3.16 a 95% confidence interval of (93.8, 102.1) was given based on a sample of n = 92 infants. Suppose, for sake of argument, that we could change the sample size and we would still get a sample mean of 97.95 and a sample SD of 20.04. How large would the sample size, n, need to be in
A group of 101 patients with end-stage renal disease were given the drug epoetin.19 The mean hemoglobin level of the patients was 10.3 (g/dl), with an SD of 0.9. Construct a 95% confidence interval for the population mean.
Use Table 3 to find the value of t0 0025 when df = ∞. (Do not attempt to interpolate in Table 4.)
Data are often summarized in this format: ± SE. Suppose this interval is interpreted as a confidence interval. If the sample size is large, what would be the confidence level of such an interval? That is, what is the chance that an interval computed as ± (l.00)SE will actually contain the
(a) If the sample size is small but the population distribution is normal, is the confidence level of the interval y ± SE larger or smaller than the answer to Exercise 6.3.21? Explain. (b) How is the answer to Exercise 6.3.21 affected if the population distribution of Y is not approximately normal?
As part of a study of the development of the thymus gland, researchers weighed the glands of five chick embryos after 14 days of incubation. The thymus weights (mg) were as follows 12:29.6 21.5 28.0 34.6 44.9For these data, the mean is 31.7 and the standard deviation is 8.7.(a) Calculate the
Consider the data from Exercise 6.3.3. (a) Construct a 95% confidence interval for the population mean. (b) Interpret the confidence interval you found in part (a). That is, explain what the numbers in the interval mean.
Six healthy 3-year-old female Suffolk sheep were injected with the antibiotic Gentamicin, at a dosage of 10 mg/kg body weight. Their blood serum concentrations (µg/ml) of Gentamicin 1.5 hours after injection were as follows13:33 26 34 31 23 25For these data, the mean is 28.7 and the standard
A zoologist measured tail length in 86 individuals, all in the 1-year age group, of the deermouse Peromyscus. The mean length was 60.43 mm and the standard deviation was 3.06 mm. A 95% confidence interval for the mean is (59.77,61.09).(a) True or false (and say why): We are 95% confident that the
Refer to Exercise 6.3.6. (a) Without doing any computations, would an 80% confidence interval for the data in Exercise 6.3.6 be wider, narrower, or about the same? Explain. (b) Without doing any computations, if 500 mice were sampled rather than 86, would the 95% confidence interval listed in
Researchers measured the bone mineral density of the spines of 94 women who had taken the drug CEE. (See Example 6.3.4, which dealt with hip bone mineral density.) The mean was 1.016 g/cm2 and the standard deviation was 0.155 g/cm2. A 95% confidence interval for the mean is (0.984,1.048). (a) True
An experiment is being planned to compare the effects of several diets on the weight gain of beef cattle, measured over a 140-day test period.20 In order to have enough precision to compare the diets, it is desired that the standard error of the mean for each diet should not exceed 5 kg. (a) If the
A medical researcher proposes to estimate the mean serum cholesterol level of a certain population of middle-aged men, based on a random sample of the population. He asks a statistician for advice. The ensuing discussion reveals that the researcher wants to estimate the population mean to within
Suppose you are planning an experiment to test the effects of various diets on the weight gain of young turkeys. The observed variable will be Y = weight gain in 3 weeks (measured over a period starting 1 week after hatching and ending 3 weeks later). Previous experiments suggest that the standard
A study of 29 female Sumatran elephants provided a 95% confidence interval for the mean shoulder height as (197.2, 235.1) cm.24 Consider a new study to estimate the mean shoulder height of male Sumatran elephants. Assuming the standard deviations of shoulder heights are similar for males and
A researcher is planning to compare the effects of two different types of lights on the growth of bean plants. She expects that the means of the two groups will differ by about 1 inch and that in each group the standard deviation of plant growth will be around 1.5 inches. Consider the guideline
SGOT is an enzyme that shows elevated activity when the heart muscle is damaged. In a study of 31 patients who underwent heart surgery, serum levels of SGOT were measured 18 hours after surgery.30 The mean was 49.3 U/l and the standard deviation was 68.3 U/l. If we regard the 31 observations as a
A dendritic tree is a branched structure that emanates from the body of a nerve cell. In a study of brain development, researchers examined brain tissue from seven adult guinea pigs. The investigators randomly selected nerve cells from a certain region of the brain and counted the number of
In an experiment to study the regulation of insulin secretion, blood samples were obtained from seven dogs before and after electrical stimulation of the vagus nerve. The following values show, for each animal, the increase (after minus before) in the immunoreactive insulin concentration (µU/ml)
In a study of parasite-host relationships, 242 larvae of the moth Ephestia were exposed to parasitization by the Ichneumon fly. The following table shows the number of Ichneumon eggs found in each of the Ephestia larva.33For these data, = 2.368 and s = 1.950. Student's t method yields the following
The following normal quantile plot shows the distribution of the diameters, in cm, of each of nine American Sycamore trees. 34The normal quantile plot is not linear, which suggests that a transformation of the data is needed before a confidence interval can be constructed using Student's t method.
Four treatments were compared for their effect on the growth of spinach cells in cell culture flasks. The experimenter randomly allocated two flasks to each treatment. After a certain time on treatment, he randomly drew three aliquots (1 cc each) from each flask and measured the cell density in
In an experiment on soybean varieties, individually potted soybean plants were grown in a greenhouse, with 10 plants of each variety used in the experiment. From the harvest of each plant, five seeds were chosen at random and individually analyzed for their percentage of oil. This gave a total of
In a plant mitigation project, an entire local (endangered) population of 255 Congdon's tar plants was transplanted to a new location.35 One year after transplant, 30 of the 255 plants were randomly selected and the diameter at the root caudix junction (the top of the root just beneath the surface
Data from two samples gave the following results:Compute the standard error of (1 - 2)
Compute the standard error of (1 - 2) for the following data:
Compute the standard error of (1 - 2) for the following data:
Consider the data from Exercise 6.6.3. Suppose the sample size were doubled, but the means and SDs stayed the same as follows. Compute the standard error of (1 - 2 )
Data from two samples gave the following results:Compute the standard error of (1 - 2 ).
Example 6.6.3 reports measurements of pain for children who have had their tonsils removed. Another variable measured in that experiment was the number of the same, doses of Tylenol taken by the children in the two groups. Those data are Compute the standard error of (1 - 2)
8 Two varieties of lettuce were grown for 16 days in a controlled environment. The following table shows the total dry weight (in grams) of the leaves of nine plants of the variety "Salad Bowl" and six plants of the variety "Bibb."38Compute the standard error of (1 - 2) for these data.
In Table 6.6.3, data were presented from an experiment that compared two types of surgery. The average pain score of the 49 children given conventional tonsillectomies was 4.3, with an SD of 2.8. For the 52 children in the Coblation group the average was 1.9 with an SD of 1.8. Use these data to
Consider the experiment described in Exercise 6.7.9. For the same subjects, the change in diastolic blood pressure was 1.1 mm Hg greater, on average, for the subjects on the fruits-and-vegetables diet than for subjects on the standard diet. A 97.5% confidence interval for the difference between the
Researchers were interested in the short-term effect that caffeine has on heart rate. They enlisted a group of volunteers and measured each person's resting heart rate. Then they had each subject drink 6 ounces of coffee. Nine of the subjects were given coffee containing caffeine, and 11 were given
Consider the data from Exercise 6.7.11. Given that there are only a small number of observations in each group, the confidence interval calculated in Exercise 6.7.11 is only valid if the underlying populations are normally distributed. Is the normality condition reasonable Bere? Support your answer
A researcher investigated the effect of green light, in comparison to red light, on the growth rate of bean plants. The following table shows data on the heights of. plants (in inches) from the soil to the first branching stem. 2 weeks after germination.48 Use these data to construct a 95%
6.7.15 Researchers reported the mean ± SE foot circumferences of many male and female Sumatran elephants as 125.6 ± 4.4 cm for the males and 151.7 ± 3.3 for the females.24 You may assume that at least 20 of each sex were sampled.(a) Compute an approximate 95% confidence
Ferulic acid is a compound that may play a role in disease resistance in corn. A botanist measured the concentration of soluble ferulic acid in corn seedlings grown in the dark or in a light/dark photoperiod. The results (nmol acid per gm tissue) were as shown in the table.41(a) Construct a 95%
A study was conducted to determine whether relaxation training, aided by biofeedback and meditation, could help in reducing high blood pressure. Subjects were randomly allocated to a biofeedback group or a control group. The biofeedback group received training for 8 weeks. The table reports the
Prothrombin time is a measure of the clotting ability of blood. For 10 rats treated with an antibiotic and 10 control rats, the prothrombin times (in seconds) were reported as follows43:(a) Construct a 90% confidence interval for the difference in population means. (Assume that the two populations
The accompanying table summarizes the sucrose consumption (mg in 30 minutes) of black blowflies injected with Pargyline or saline (control).44(a) Construct a 95% confidence interval for the difference in population means. (b) Repeat part (a) using a 99% level of confidence.
In a field study of mating behavior in the Mormon cricket (Anabrus simplex), a biologist noted that some females mated successfully while others were rejected by the males before coupling was complete. The question arose whether some aspect of body size might play a role in mating success. The
In an experiment to assess the effect of diet on blood pressure, 154 adults were placed on a diet rich in fruits and vegetables. A second group of 154 adults was placed on a standard diet. The blood pressures of the 308 subjects were recorded at the start of the study. I Light weeks later, the
To study the conversion of nitrite to nitrate in the blood, researchers injected four rabbits with a solution of radioactively labeled nitrite molecules. Ten minutes after injection, they measured for each rabbit the percentage of the nitrite that had been converted to nitrate.The results were as
Researchers measured the number of tree species in each of 69 vegetational plots in the Lama Forest of Benin, West Africa.53 The number of species ranged from a low of 1 to a high of 12. The sample mean was 6.8 and the sample SD was 2.4, which results in a 95% confidence interval of (6.2,7.4).
As part of a study of natural variation in blood chemistry, serum potassium concentrations were measured in 84 healthy women. The mean concentration was 4.36 mEq/1, and the standard deviation was 0.42 mEq/1. The table presents a frequency distribution of the data.54(a) Calculate the standard error
Refer to Exercise 6.S.11. In medical diagnosis, physicians often use "reference limits" for judging blood chemistry values; these are the limits within which we would expect to find 95% of healthy people. Would 'a 95% confidence interval for the mean be a reasonable choice of "reference limits" for
Refer to Exercise 6.S. 11. Suppose a similar study is to be conducted next year, to include serum potassium measurements on 200 healthy women. Based on the data in Exercise 6.S. 11, what would you predict would be (a) The SD of the new measurements? (b) The SE of the new measurements?
An agronomist selected six wheat plants at random from a plot, and then, for each plant, selected 12 seeds from the main portion of the wheat head; by weighing, drying, and reweighing, she determined the percentage moisture in each batch of seeds. The results were as follows55:62.7 63.6 60.9 63.0
As part of the National Health and Nutrition Examination Survey (NHANES). hemoglobin levels were checked for a sample of 1139 men age 70 and over.56 The sample mean was 145.3 g/1 and the standard deviation was 12.87 g/1.(a) Use these data to construct a 95% confidence interval for LL.(b) Does the
The following data are 16 weeks of weekly fecal coliform counts (MPN/100 ml) at Dairy Creek in San Luis Obispo County, California.57 203 215 240 236 217 296 301 190 197 203 210 215 270 290 310 287 (a) Counts above 225 MPN/l00ml are considered unsafe. What type of one-sided interval (upper- or
The blood pressure (average of systolic and diastolic measurements) of each of 38 persons were measured.58 The average was 94.5 (mm Hg). A histogram of the data is shown.Which of the following is an approximate 95% confidence interval for the population mean blood pressure? Explain. (i) 94.5
Suppose you wished to estimate the mean blood pressure of students at your school to within 2 mmHg with 95% confidence. (a) Using the data displayed in Exercise 6.S.17 as pilot data for your study, determine the (approximate) sample size necessary to achieve your goals. (b) Suppose your school is a
The diameter of the stem of a wheat plant is an important trait because of its relationship to breakage of the stem, which interferes with harvesting the crop. An agronomist measured stem diameter in eight plants of the Tetrastichon cultivar of soft red winter wheat. All observations were made 3
Is the nutrition information on commercially produced food accurate? In one study, researchers sampled 13 packages of a certain frozen reduced-calorie chicken entree with a reported calorie content of 252 calories per package. The mean calorie count of the sampled entrees was 306 with a sample
Nitric oxide is sometimes given to newborns who experience respiratory failure. In one experiment, nitric oxide was given to 114 infants with respiratory failure. This group was compared to a control group of 121 infants with respiratory failure. The length of hospitalization (in days) was recorded
Consider the data from Exercise 6.S.20(a) which led to a 95% confidence interval for μ1, - μ2 of (-2.3,16.1). (a) True or false (and say why)^We are 95% confident that the difference between 1 and 2 is between -2.3 days and 16.1 days. (b) True or false (and say why): If this experiment were
Refer to Exercise 6.S.2.(a) What conditions are needed for the confidence interval to be valid?(b) Are these conditions met? How do you know?(c) Which of these conditions is most important?
Refer to Exercise 6.S.2. Suppose that the data on the eight plants are regarded as a pilot study, and the agronomist now wishes to design a new study for which he wants the standard error of the mean to be only 0.03 mm. How many plants should be measured in the new study?
A sample of 20 fruitfly (Drosophila melanogaster) larva were incubated at 37°C for 30 minutes. It is theorized that such exposure to heat causes polytene chromosomes located in the salivary glands of the fly to unwind, creating puffs on the chromosome arm that are visible under a microscope.
Over a period of about 9 months, 1,353 women reported the timing of each of their menstrual cycles. For the first cycle reported by each woman, the mean cycle time was 28.86 days, and the standard deviation of the 1,353 times was 4.24 days.52 (a) Construct a 99% confidence interval for the
Refer to the menstrual cycle data of Exercise 6.S.6.(a) Over the entire time period of the study, the women reported a total of 12,247 cycles. When all of these cycles are included, the mean cycle time is 28.22 days. Explain why one would expect that this mean would be smaller than the value 28.86
For the 28 lamb birth weights of Example 6.2.2, the mean is 5.1679 kg, the SD is 0.6544 kg, and the SE is 0.1237 kg. (a) Construct a 95% confidence interval for the population mean. (b) Construct a 99% confidence interval for the population mean. (c) Interpret the confidence interval you found in
Refer to Exercise 6.S.8. (a) What conditions are required for the validity of the confidence intervals? (b) Which of the conditions of part (a) can be checked (roughly) from the histogram of Figure 6.2.1? (c) Twin births were excluded from the lamb birthweight data. If twin births had been
Suppose we have samples of five men and of five women and have conducted a randomization test to compare the sexes on the variable Y = pulse. Further, suppose we have found that in 120 out of the 252 possible outcomes under randomization the difference in means is at least as large as the
In an investigation of the possible influence of dietary chromium on diabetic symptoms, some rats were fed a low-chromium diet, and others were fed a normal diet. One response variable was activity of the liver enzyme GITH, which was measured using a radioactively labeled molecule. The accompanying
The following table shows the number of bacteria colonies present in each of several petri dishes, after E. coli bacteria were added to the dishes and they were incubated for 24 hours. The "soap" dishes contained a solution prepared from ordinary soap; the "control" dishes contained a solution of
Consider two samples of sizes n1 = 5, n2 = 7. Use Table 6 to find the P-value, assuming that HA is non-directional and that (a) Us = 26 (b) Us = 30 (c) Us = 35
Consider two samples of sizes n1 = 4, n2 = 8. Use Table 6 to find the P-value, assuming that HA is non-directional and that (a) Us = 25 (b) Us = 31 (c) Us = 32
In a pharmacological study, researchers measured the concentration of the brain chemical dopamine in six rats exposed to toluene and six control rats. (This is the same study described in Example 7.2.1.) The concentrations in the striatum region of the brain were as shown in the table.4(a) Use a
In a study of hypnosis, breathing patterns were observed in an experimental group of subjects and in a control group. The measurements of total ventilation (liters of air per minute per square meter of body area) are shown. (These are the same data that were summarized in Exercise 7.5.6.) Use a
In an experiment to compare the effects of two different growing conditions on the heights of greenhouse chrysanthemums, all plants grown under condition 1 were found to be taller than any of those grown under condition 2 (i.e., the two height distributions did not overlap). Calculate the value of
In a study of preening behavior in the fruitfly Drosophila melanogaster, a single experimental fly was observed for 3 minutes while in a chamber with 10 other flies of the same sex. The observer recorded the timing of each episode ("bout") of preening by the experimental fly. This experiment was
Substances to be tested for cancer-causing potential are often painted on the skin of mice. The question arose Whether mice might get an additional dose of the substance by licking or biting their cagemates. To answer this question, the compound benzo(a)pyrene was applied to the backs of 10 mice: 5
Human beta-endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. An exercise physiologist measured the resting (unstressed) blood concentration of HBE in two groups of men: Group 1 consisted of 11 men who had been jogging regularly for some time, and group 2
Below are normal probability plots of the HBE data from Exercise 7.10.8.(a) Using the plots to support your answer, is there evidence of abnormality in either of the samples?(b) Considering your answer to (a) and the preceding plots, should we conclude that the data are indeed normally distributed?
For each of the following data sets, use Table 4 to bracket the two-tailed P-value of the data as analyzed by the t test.(a)(b)(c)
In a study of the development of the thymus gland, researchers weighed the glands of 10 chick embryos. Five of the embryos had been incubated 14 days, and five had been incubated 15 days. The thymus weights were as shown in the table.(a) Use a t test to compare the means at Î± =
As part of an experiment on root metabolism, a plant physiologist grew birch tree seedlings in the greenhouse. He flooded four seedlings with water for one day and kept four others as controls. He then harvested the seedlings and analyzed the roots for ATP content. The results (nmol ATP per mg
After surgery a patient's blood volume is often depleted. In one study, the total circulating volume of blood plasma was measured for each patient immediately after surgery. After infusion of a "plasma expander" into the bloodstream, the plasma volume was measured again and the increase in plasma
Nutritional researchers conducted an investigation of two high-fiber diets intended to reduce serum cholesterol level. Twenty men with high serum cholesterol were randomly allocated to receive an "oat" diet or a "bean" diet for 21 days. The table summarizes the fall (before minus after) in serum
Suppose we have conducted a t test, with α = 0.05 and the P-value is 0.03. For each of the following statements, say whether the statement is true or false and explain why. (a) We reject H0 with α = 0.05. (b) We have significant evidence for HA with α = 0.05. (c) We would reject H0 if a were
Suppose we have conducted a t test, with α = 0.10 and the P-value is 0.07. For each of the following statements, say whether the statement is true or false and explain why. (a) We reject H0 with α = 0.10. (b) We have significant evidence for HA with α = 0.10. (c) We would reject H0 if a were
The following table shows the number of bacteria colonies present in each of several petri dishes after E. coli bacteria were added to the dishes and they were incubated for 24 hours. The "soap" dishes contained a solution prepared from ordinary soap; the "control" dishes contained a solution of
Researchers studied the effect of a houseplant fertilizer on radish sprout growth. They randomly selected some radish seeds to serve as controls, while others were planted in aluminum planters to which fertilizer sticks were added. Other conditions were held constant between the two groups. The
A scientist recorded the tail lengths (in cm) of two varieties of woodland salamanders: red-backed and lead-backed. The table below shows summary values.(a) What is the value of the t test statistic for comparing the means? (b) In the context of this study, state the null and alternative
For each of the following data sets, use Table 4 to bracket the two-tailed P-value of the data as analyzed by the t test.(a)(b) (c)
For each of the following situations, suppose H0: µ1 = µ2 is being tested against HA: µ1 ≠ µ2. State whether or not there is significant evidence for HA. (a) P-value = 0.085, α = 0.10. (b) P-value = 0.065, α = 0.05. (c) ts = 3.75 with 19 degrees of freedom, α = 0.01. (d) ts = 1.85 with 12
For each of the following situations, suppose H0: µ1 ≠ µ2 is being tested against HA: µ1 ≠ µ2.-State whether or not there is significant evidence for HA. (a) P-value = 0.046, α = 0.02. (b) P-value = 0.033, α = 0.05. (c) ts = 2.26 with 5 degrees of freedom, α = 0.10. (d) ts = 1.94 with 16
In a study of the nutritional requirements of cattle, researchers measured the weight gains of cows during a 78-day period. For two breeds of cows, Hereford (HH) and Brown Swiss/Hereford (SH), the results are summarized in the following table.(a) What is the value of the t test statistic for
Backfat thickness is a variable used in evaluating the meat quality of pigs. An animal scientist measured backfat thickness (cm) in pigs raised on two different diets, with the results given in the table.Consider using the t test to compare the diets. Bracket the P-value, assuming that the number
Heart disease patients often experience spasms of the coronary arteries. Because biological amines may play a role in these spasms, a research team measured amine levels in coronary arteries that were obtained postmortem from patients who had died of heart disease and also from a control group of
In a study of the periodical cicada (Magicicada septendecim), researchers measured the hind tibia lengths of the shed skins of 110 individuals. Results for males and females are shown in the accompanying table.(a) Use a t test to investigate the association of tibia length on gender in this
Myocardial blood flow (MBF) was measured for two groups of subjects after 5 minutes of bicycle exercise. The normoxia ("normal oxygen") group was provided normal air to breath whereas the hypoxia group was provided with a gas mixture with reduced oxygen, to simulate high altitude. The results
Consider the study in Exercise 7.3.10. Since the P-value was so large, do the data provide compelling evidence that the treatments are equally effective?

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