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

Consider the study design and summary data presented in Exercise 12.2.7 to examine the relationship between fungus growth and latisaric acid concentration. (a) Is this study an observational study or an experiment? (b) It is suggested that acid could be used to retard fungus growth. Could these
To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass for each of seven men. They also measured the total 24-hour energy expenditure for each man during conditions of quiet sedentary activity. The
In a study of protein synthesis in the oocyte (developing egg cell) of the frog Xenopus laevis, a biologist injected individual oocytes with radioactively labeled leucine. At various times after injection, he made radioactivity measurements and calculated how much of the leucine had been
The peak How rate of a person is the fastest rate at which the person can expel air after taking a deep breath. Peak flow rate is measured in units of liters per minute and gives an indication of the person's respiratory health. Researchers measured peak flow rate and height for each of a sample of
For each of the following data sets, prepare a plot like Figure 12.3.8, showing the data, the fitted regression line, and two lines whose vertical distance above and below the regression line is se. What percentage of the data points are within +se of the regression line? What percentage of the
Suppose a large sample of (x, y) pairs were used to fit the regression of Y on X. Now suppose we observed 100 further (x, y) pairs. About how many of these new observations would you expect to be farther than 2se from the regression line?
Forced expiratory volume (FEV) is a measure of the rate of airflow (L/min) during one deep exhalation. FEV was measured for each of 60 students between 65 and 73 inches tall. The scatterplot below shows FEV plotted against height. The triangles in the plot are the average FEV values for each
Consider the leucine data and summaries presented in Exercise 12.3.1. (a) Predict the amount of leucine incorporated at 45 minutes. (b) Calculate the residual associated with data point (50, 1.50).
In an investigation of the physiological effects of alcohol (ethanol), 15 mice were randomly allocated to three treatment groups, each to receive a different oral dose of alcohol. The dosage levels were 1.5, 3.0, and 6.0 gm alcohol per kg body weight. The body temperature of each mouse was measured
Consider the cob weight data from Exercise 12.2.6. (a) Use the summaries in Exercise 12.2.6 to calculate the fitted regression line and approximate residual standard deviation. (b) Interpret the value of the slope of the regression line, b1, in the context of this setting. (c) SS(resid) = 1337.3.
Consider the Fungus growth data from Exercise 12.2.7. (a) Calculate the linear regression of Y on X. (b) Plot the data and add the regression line to your graph. Does the line appear to fit the data well? (c) SS(resid) = 16.7812. Use this to compute se. What are the units of se? (d) Draw a ruler
Consider the Energy Expenditure data from Exercise 12.2.9. (a) Calculate the linear regression of Y on X. (b) Plot the data and add the regression line to your graph. Does the line appear to fit the data well? (c) Interpret the value of the slope of the regression line. b1, in the context of this
The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory, and
Scientists studied the relationship between the length of the body of a bullfrog and how far it can jump. Eleven bullfrogs were included in the study. The results are given in the table.16(a) Calculate the linear regression of Y on X.(b) Interpret the value of the slope of the regression line. b1,
Consider the bullfrog jump data and summaries presented in Exercise 12.3.8. (a) Predict the maximum jump for a frog that is 152 mm long. (b) Assuming the residuals follow a normal model, would it be unusual for a 152 mm long frog to jump 145cm?
For the data in Exercise 12.2.7 there were two observations for which X = 0. The average response (Y value) for these points is 33.3 + 31.0/2 = 32.15. However, the intercept of the regression line, b0 is not 32.15. Why not? Why is b0 a better estimate of the average fungus growth when laetisaric
Refer to the body temperature data of Exercise 12.3.3. Assuming that the linear model is applicable, estimate the mean and the standard deviation of the drop in body temperature that would be observed in mice given alcohol at a dose of 2 gm/kg. [Tip: Is the X variable dose or log(dose)?]
Refer to the cob weight data of Exercises 12.2.6 and 12.3.4. Assume that the linear model holds. (a) Estimate the mean cob weight to be expected in a plot containing (i) 100 plants; (ii) 120 plants. (b) Assume that each plant produces one cob. How much grain would we expect to get from a plot
For the cob weight data, SS(resid) = 1,337.3. Estimate the standard deviation of cob weight in plots containing (i) 100 plants; (ii) 120 plants.
Refer to the fungus growth data of Exercise 12.2.7. For these data, SS(resid) = 16.7812. Assuming that the linear model is applicable, find estimates of the mean and standard deviation of fungus growth at a laetisaric acid concentration of 15 pg/ml.
Refer to the energy expenditure data of Exercise 12.2.9. Assuming that the linear model is applicable, estimate the 24-hour energy expenditure of a man whose fat-free mass is 55 kg.
Refer to the Ca pump activity of Exercise 12.2.10. For these data SS(resid) = 21,984,623.(a) Assuming that the linear model is applicable, estimate the mean and standard deviation basal Ca pump activity for children born to mothers with a hair Hg level of 3 pg/g.(b) Using the values computed in
Refer to the bullfrog data of Exercise 12.3.8. Assuming that the linear model is applicable, estimate the maximum jump length of a bullfrog whose body length is 150 mm.
Refer to the peak flow data of Exercise 12.3.10. Assuming that the linear model is applicable, find estimates of the mean and standard deviation of peak flow for men 180 cm tall.
Refer to the leucine data given in Exercise 12.3.1.(a) Construct a 95% confidence interval for B\.(b) Interpret the confidence interval from part (a) in the context of this setting.
Scientists recorded the dry weight (mg) and corolla diameter (cm) of 86 evening primrose (O. har-ringtonii) flowers growing in a natural habitat.21(a) Use the following computer output, from fitting a regression model, to construct a 95% confidence interval for Î²1.(b) Interpret the
Refer to the body temperature data of Exercise 12.3.3. For these data, se = 0.91472. Construct a 95% confidence interval for β1.
Refer to the cob weight data of Exercise 12.2.6. For these data, SS(resid) = 1,337.3. (a) Construct a 95% confidence interval for B\. (b) Interpret the confidence interval from part (a) in the context of this setting.
Refer to the fungus growth data of Exercise 12.2.7. For these data. SS(resid) = 16.7812. (a) Calculate the standard error of the slope, SEbl. (b) Consider the null hypothesis that laetisaric acid has no effect on growth of the fungus. Assuming that the linear model is applicable, state in symbols
Refer to the energy expenditure data of Exercise 12.2.9. For these data, SS(resid) = 21,026.1. (a) Construct a 95% confidence interval for B\. (b) Construct a 90% confidence interval for B\.
Refer to the basal Ca pump data from Exercise 12.2.10. For these data, se = 548.78. (a) Construct a 95% confidence interval for β1. (b) What do you think about a claim that β1 is less than -800 (nmol/mg/hr )/(ug/g)? Use your interval from part (a) to support your answer. (c) What do you think
Refer to the respiration data of Exercise 12.3.7. Assuming that the linear model is applicable, test the null hypothesis of no relationship against the alternative that trees from higher altitudes tend to have higher respiration rates. Let a = 0.05.
The following computer output is from fitting a regression model to the snake length data of Example 12.2.2.The regression equation isWeight = -301 + 7.19 Lengths = 12.50 R-sq = 89.1% R-sq(adj) = 87.5% Analysis of Variance (a) Use the output to construct a 95% confidence interval for
Refer to the peak flow data of Exercise 12.3.10. Assume that the linear model is applicable. (a) lest the null hypothesis of no relationship against the alternative that peak flow is related to height. Use a non directional alternative with a = 0.10. (b) Repeat the test from part (a), but this time
In a metabolic study, four male swine were tested three times: when they weighed 30 kg, again when they weighed 60 kg, and again when they weighed 90 kg. During each test, the experimenter analyzed feed intake and fecal and urinary output for 15 days, and from these data calculated the nitrogen
Refer to the energy expenditure data of Exercise 12.2.9. Each subject's expenditure value (V) is the average of two measurements made on different occasions. It might be proposed that it would be better to use the two measurements as separate data points, thus yielding 14 observations rather than
In the following scatterplot of the Ca pump data of Exercise 12.2.10, one of the points is marked with an "X." In addition, there are two regression lines on the plot: The solid line includes all of the data and the dashed line omits the point marked "X."(a) Would we consider the point marked "X"
The following three residual plots, (i), (ii). and (iii), were generated after fitting regression lines to the following three scatterplots. (a), (b), and (c). Which resid¬ual plot goes with which scatterplot? How do you know?(a)(b) (c) (i) (ii) (iii)
The following two residual plots, (i), and (ii), were generated after fitting regression lines to the two scatter-plots (a) and (b). Which residual plot goes with which scatterplot? How do you know?
Sketch the residual plot that would be produced by fitting a regression line to the following scatterplot. One of the points is plotted with an "X." Indicate this point on the residual plot.
(Computer exercise) Researchers measured the diameters of 20 trees in a central Amazon rain forest and used 14C-dating to determine the ages of these trees. The data are given in the following table.27 Consider the use of diameter, X, as a predictor of age, Y.(a) Make a scatterplot of Y = age
In a study of heat stress on cows, researchers measured the rectal temperature (°C) for 1,280 lactating cows (Y) and relative humidity (%) (A*).28 The following graph displays the data and regression line (solid line). There are two other pairs of lines on this graph: dashed and dotted. One
(Continuation of 12.7.1) Suppose 5,000 additional cows were included in the sample and a similar plot of the data, regression line, confidence and prediction bands were made of this new larger sample. Would the prediction band get much narrower? Explain your reasoning.
The following graph displays the regression line and 95% confidence and prediction bands for the peak respiration flow data from Exercise 12.3.10.(a) Using the graph to justify your answer, would it be very surprising to find a 195-cm-tall individual with a peak How rate above 900 l/min? (b) Using
Biologists took a sample of 20 male toads and measured body length (snout-vent length, in mm) of each of them. They also recorded how deep the pitch was of each toad's croak (call, measured in Hz). Larger toads had deeper pitched croaks, as the scatterplot below shows. The graph shows a regression
In a study of the Mormon cricket (Anabrus simplex), the correlation between female body weight and ovary weight was found to be r = 0.836. The standard deviation of the ovary weights of the crickets was 0.429 g. Assuming that the linear model is applicable, estimate the standard deviation of ovary
An exercise physiologist used skinfold measurements to estimate the total body fat, expressed as a percentage of body weight, for 19 participants in a physical fitness program. The body fat percentages and the body weights are shown in the table.36Actually, participants 1 to 10 are men, and
Refer to the respiration rate data of Exercise 12.3.7. Construct a 95% confidence interval for β1.
The following plot is a residual plot from fitting a regression model to some data. Make a sketch of the scatterplot of the data that led to this residual plot. (There are two possible scatterplots -one in which b1 is positive and one in which b1 is negative.)
Biologists studied the relationship between embryonic heart rate and egg mass for 20 species of birds. They found that heart rate, Y, has a linear relationship with the logarithm of egg mass, X. The data are given in the following table.37For these data the fitted regression equation
An ornithologist measured the mass (g) and head length (the distance from the tip of the bill to the back of the skull, in mm) for a sample of 60 female blue jays. Here is a plot of the data and computer output:Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error:
Consider the study and regression output in Exercise 12.S.14. The P-value given on the "Head" line is 0.00000595. (a) What hypothesis is being tested using this P-value? State your answer symbolically and in plain English. (b) What conditions are necessary for the P-value to be trustworthy?
Consider the study and regression output in Exercise 12.S.14. Sadly, an ornithologist's cat brought in just the head of a blue jay. The head length was 47 mm. What would you predict the mass of the bird to have been? Is your prediction trustworthy? Explain.
In a study of crop losses due to air pollution, plots of Blue Lake snap beans were grown in open-top field chambers, which were fumigated with various concentrations of sulfur dioxide. After a month of fumigation, the plants were harvested, and the total yield of bean pods was recorded for each
Consider the study and regression output in Exercise 12.S.14. Using only the numeric output to support your answer, would it be unusual for a female blue jay with a head length of 52 mm to weigh less than 54 g?
The accompanying table gives two data sets: (A) and (B).The values of X are the same for both data sets and are given only once.(a) Generate scatterplots of the two data sets. (b) For each data set (i) estimate r visually and (ii) calculate r. (c) For data set (a), multiply the values of A" by 10,
This exercise shows the power of scatterplots to reveal features of the data that may not be apparent from the ordinary linear regression calculations. The accompanying table gives three fictitious data sets. A, B, and C. The values of X are the same for each data set, but the values of V are
In a pharmacological study, 12 rats were randomly allocated to receive an injection of amphetamine at one of two dosage levels or an injection of saline. Shown in the table is the water consumption of each animal (ml water per kg body weight) during the 24 hours following injection.39(a) Calculate
Consider the Amazon tree data from Exercise 12.6.9. The researchers in this study were interested in how age, Y, is related to X = "growth rate," where growth rate is defined as diameter/age (i.e., cm of growth per year). (a) Create the variable "growth rate" by dividing each diameter by the
Researchers measured the blood pressures of 22 students in two situations: when the students were relaxed and when the students were taking an important examination. The table lists the systolic and diastolic pressures for each student in each situation.40(a) Compute the change in systolic pressure
Consider the data from Exercise 12.S.25, part (f). (a) Construct a 95% confidence interval for B\. (b) Interpret the confidence interval from part (a) in the context of this setting.
Selenium (Se) is an essential element that has been shown to play an important role in protecting marine mammals against the toxic effects of mercury (Hg) and other metals. It has been suggested that metal concentrations in marine mammal teeth can potentially be used as bioindicators for body
(Continuation of 12.S.27) The following are summary statistics for the selenium data in Exercise 12.S.27. = 20.685 = 156.599 sX = 13.4491 sY = 36.0595 r = 0.53729 SS(resid) = 17,573.4 (a) Calculate the regression line of Tooth selenium on Liver selenium. (b) Compute a 95% confidence interval
Refer to Exercise 12.S.2.(a) Assuming that the linear model is applicable, find estimates of the mean and the standard deviation of yields of beans exposed to 0.24 ppm of sulfur dioxide.(b) Is the estimate in part (a) an interpolation or extrapolation? How can you tell?(c) Which condition of the
The whales observed in this study were harvested during a traditional Inuit hunt in two particular years. What are we assuming about the captured whales to justify our analyses of these data in the preceding problems?
Refer to Exercise 12.S.2. Consider the null hypothesis that sulfur dioxide concentration has no effect on yield. (a) Assuming that the linear model holds, formulate this as a hypothesis about the true regression line. (b) Write a directional alternative, in symbols, that says increasing sulfur
Another way to analyze the data of Exercise 12.S.2 is to take each treatment mean as the observation V; then the data would be summarized as in the accompanying table.(a) For the regression of mean yield on X, calculate the regression line and the residual standard deviation, and compare with the
In a study of the tufted titmouse (Parus bicolor), an ecologist captured seven male birds, measured their wing lengths and other characteristics, and then marked and released them. During the ensuing winter, he repeatedly observed the marked birds as they foraged for insects and seeds on tree
A scatterplot and fitted regression line of the data from Exercise 12.S.6 follow. The individual birds are labeled in the plot.(a) Which bird/point has the largest regression residual? (b) Which bird(s)/points(s) have the most leverage? (c) Are there any birds/points that are influential? (d)
Exercise 12.3.7 deals with data on the relationship between body length and jumping distance of bullfrogs. A third variable that was measured in that study was the mass of each bullfrog. The following table shows these data.16Preliminary calculations yield the following results: r = 0.90521
A residual plot and normal quantile plot from the linear regression of Y on X based on the bullfrog mass data in Exercise 12.S.8 follow.Use these plots to comment on the required conditions for inference in regression. Is there any reason to substantially doubt that these conditions are met?
The growth per day (in cm) of alfalfa sprouts was recorded for 50 sprouts kept in darkness and for 49 sprouts kept in light. The log of each observation was then taken to make the distributions reasonably normal. For the darkness sample, the average was 1.40, and the SD was 0.92. For the light
Is there a relationship between wing length (mm) and wing beat frequency (Hz) among hummingbirds? In one study, researchers measured the wing lengths and wing beat frequencies of 12 hummingbirds.3 The following are basic summaries and a plot of the 12 data values.(a) If the circled point was
Consider the hummingbird data in Exercise IV.10. (a) What percentage of the variation in wing beat frequency is explained by the relationship between wing length and wing beat frequency? (b) Formally speaking, an important adjective is missing from part (a) that describes the nature of the
Consider the hummingbird data and information provided in Exercise IV. 10. (a) Find the equation of the fitted regression line. (b) Predict the wingbeat frequency for a hummingbird with 30 mm wings. (c) Predict the mean wingbeat frequency for hummingbirds with 30 mm wings. (d) Are the predictions
Consider the hummingbird data and information provided in Exercise IV.10. (a) Do longer wings tend to beat more slowly (i.e., lower frequency) than shorter wings? In plain English, what are the null and alternative hypotheses to be tested? (b) Compute the value of ts used to test the hypothesis in
The following is a plot of the residuals against the fitted values for the hummingbird data of Exercise IV.10.(a) Which point in the residual plot corresponds to the circled point in the data appearing in Exercise IV.10? How can you tell? (b) Which point in the residual plot corresponds to the
Researchers measured initial weight, X, and weight gain. V. of 15 rats on a high protein diet.1 All weights are in grams. A scatterplot of the data shows a linear relationship. The fitted regression model is y = 54.95 + 1.06x The sample correlation coefficient, r. is 0.4X9. I Tie SE of b1 is 0.526.
Researchers wanted to compare two drugs, for-moterol and salbutamol, in aerosol solution, for the treatment of patients who suffer from exercise-induced asthma.2 Patients were to take a drug, do some exercise, and then have their "forced expiratory volume" measured. There were 30 subjects
A confused researcher finds a dime on the sidewalk and wants to test H0: p = 0.5 against HA: p ≠ 0.5 where p = Pr[Heads] when tossing the coin. This dime is an ordinary coin for which p = 0.5 -but she doesn't know that. She tosses the coin 100 times, finds the P-value for a goodness-of-fit test,
A researcher collected data on a random sample of 12 breakfast cereals. He recorded x = fiber (in grams/ ounce) and y = price (in cents/ounce). A scatterplot of the data shows a linear relationship. The fitted regression model is y = 17.42 + 0.62x The sample correlation coefficient, r, is 0.23. The
Consider a regression setting in which we construct a scatterplot, fit the regression model Å·, = b0 + b1xi, and generate a residual plot.(a) Suppose the scatterplot of y versus x is as follows:Draw a sketch of the resulting residual plot. Label the axes on your graph. (b) Suppose we
A researcher measured the number of tree species per 0.1 hectare plot along the Black, Huron, and Vermilion rivers. The data are summarized in the table below:Here is a partial ANOVA table summarizing the results. (a) Find the value of the test statistic that is used to test H0. (You do not need to
(a) Consider the data from Exercise IV.7. Suppose we want to compare the Vermilion River to the average of the other two rivers. Calculate the value of the contrast. L, to measure the difference between the mean number of species (per 0.1 hectare) along the Vermilion River and the mean number of
Researchers conducted a randomized, double-blind, clinical trial in which some patients with schizophrenia were given the drug clozapine and others were given haloperidol. After one year 61 of 163 patients in the clozapine group showed clinically important improvement in symptoms, compared with 51
A sample of 15 patients was randomly split into two groups as part of a double-blind experiment to compare two pain relievers.19 The 7 patients in the first group were given Demerol and reported the following numbers of hours of pain relief:The 8 patients in the second group were given an
Consider the data of Exercise 13.2.10. Conduct an appropriate complete analysis of the data that also includes a graphical display and discussion of how the data do or do not meet the necessary conditions for validity.Exercise 13.2.10A sample of 15 patients was randomly split into two groups as
A researcher was interested in the relationship between forearm length and height. He measured the forearm lengths and heights of a sample of 16 women and obtained the following data. How might these data be (i) visualized and (ii) analyzed?
A randomized, double-blind, clinical trial was conducted on patients who had coronary angioplasty to compare the drug lovastatin to a placebo. The percentage of stenosis (narrowing of the blood vessels) following angioplasty was measured on 160 patients given lovastatin and on 161 patients given
Consider the data of Exercise 13.2.13. (a) Conduct an appropriate analysis of the data. (b) Describe a graphical procedure to visualize these data. (c) Discuss how the data likely meet the necessary conditions for validity even though you do not have access to the raw data. Exercise 13.2.13 A
Researchers studied persons who had received intravenous immune globulin (IGIV) to see if they had developed infections of hepatitis C virus (HCV). In part of their analysis, they considered doses of Gammagard (an IGIV product) received by 201 patients. They divided the patients into 4 groups
Consider the data of Exercise 13.2.15. Conduct an appropriate analysis of the data. Exercise 13.2.15 Researchers studied persons who had received intravenous immune globulin (IGIV) to see if they had developed infections of hepatitis C virus (HCV). In part of their analysis, they considered doses
Consider the data of Exercise 13.2.17. Conduct an appropriate complete analysis of the data that also includes a graphical display and discussion of how the data do or do not meet the necessary conditions for validity.Exercise 13.2.17
Consider the data of Exercise 13.2.1. Conduct an appropriate complete analysis of the data that also includes a graphical display and discussion of how the data do or do not meet the necessary conditions for validity. Exercise 13.2.1 Researchers conducted a randomized, double-blind, clinical trial
Consider the data of Exercise 13.2.19. Conduct an appropriate complete analysis of the data that also includes a graphical display and discussion of how the data do or do not meet the necessary conditions for validity. Exercise 13.2.19 As part of a large experiment, researchers planted 2,400 sweet
A group of female college students were divided into three groups according to upper body strength. Their leg strength was tested by measuring how many consecutive times they could leg press 246 pounds before exhaustion. (The subjects were allowed only one second of rest between consecutive lifts.)
Consider the data of Exercise 13.2.21. Conduct an appropriate complete analysis of the data that also includes a graphical display and discussion of how the data do or do not meet the necessary conditions for validity.Exercise 13.2.21
Consider the data of Exercise 13.2.23. Conduct an appropriate analysis of the data to investigate whether or not some mammals (based on classification by diet) are more vulnerable to being hit than others. In addition, discuss how the data do or do not meet the necessary conditions for
A biologist collected data on the height (in inches) and peak expiratory flow (PEF-a measure of how much air a person can expire, measured in l/min) for 10 women. Here are the data:Is PEF related to height? Identify the type of statistical method that is appropriate for these data and this
Consider the data of Exercise 13.2.3. Maria is 1 inch taller than Anika. Using the information from Exercise 13.2.3, how much greater would you predict Maria's PEF to be than Anika's?Exercise 13.2.3

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