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statistics

Questions and Answers of Statistics

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
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
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
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
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.
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
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
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
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
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
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
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
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)
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
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,
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
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
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
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
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
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
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
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
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
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) =
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
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
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
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 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
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
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
(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
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
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).
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
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
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
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
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
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
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
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
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
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
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
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
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.,
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
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
(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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
(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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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