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Questions and Answers of Statistics

In a randomized clinical trial. 154 women with breast cancer were assigned to receive chemotherapy. Another 164 women were assigned to receive chemotherapy combined with radiation therapy. Survival
Refer to the data in Exercise 10.S.8.(a) Calculate the sample odds ratio.(b) Find a 95% confidence interval for the population value of the odds ratio.Exercise 10.S.8In a randomized clinical trial.
Randomly chosen college students were asked if they could touch their nose with their tongue. Six out of 53 men said yes, compared to 15 out of 56 women. (a) Use these data to construct a 95%
State whether the following statements are true or false and explain why. (a) It is more difficult to estimate a population proportion precisely if its value is near 0.50. (b) A χ2 goodness-of-fit
A random sample of 46 college students were asked if they were doing community service work during a particular semester. The following table gives the data, comparing men and women. Do the data
A researcher planted various kinds of seeds and recorded whether or not they germinated within 5 weeks. The following table gives the data.(a) Consider the null hypothesis that type of seed is
In a study of the effect of oral contraceptives on thromboembolic disease (blood clots) 175 pairs of women were studied. The pairs were matched on age, race, and other variables. Within each pair one
You think that approximately 25% of the members of a certain population smoke, but you want to take a sample in order to make an estimate. You want the standard error of to be no greater than
Before connecting the encoder and decoder rats, the researchers wanted to verify that the decode rats were sufficiently trained to choose the correct lever when seeing a visual cue. After training,
Once a brain-to-brain connection was established, a pair of rats would undergo 50 lever-pressing trials. At each trial, the researchers would record whether or not the encoder rat pressed the
Consider the research question: Does the decoder rat do what the encoder rat does? That is, when the encoder is correct, is the decoder also correct, and when the encoder is wrong, is the decoder
The study described above was actually carried out on four pairs of connected rats. The table below summarizes the results from the 200 (50 Ã— 4) trials.The value of Ï‡2s =
The accompanying table shows fictitious data for three samples.(a) Compute SS(between) and SS(within).(b) Compute SS(total), and verify the relationship between SS(between), SS(within), and
Proceed as in Exercise 11.2.1 for the following data:(a) Compute SS(between) and SS(within).(b) Compute SS(total), and verify the relationship between SS(between), SS(within), and SS(total).(c)
For the following data, SS(within) = 116 and SS(total) = 338.769.(a) Find SS(between). (b) Compute MS(between), MS(within), and spooled.
The following ANOVA table is only partially completed.(a) Complete the table.(b) How many groups were there in the study?(c) How many total observations were there in the study?
The following ANOVA table is only partially completed.(a) Complete the table.(b) How many groups were there in the study?(c) How many total observations were there in the study?
The following ANOVA table is only partially completed.(a) Complete the table.(b) How many groups were there in the study?(c) How many total observations were there in the study?
Invent examples of data with (a) SS(between) = 0 and SS(within) > 0 (b) SS(between) > 0 and SS(within) = 0 For each example, use three samples, each of size 5.
Monoamine oxidase (MAO) is an enzyme that is thought to play a role in the regulation of behavior. To see whether different categories of patients with schizophrenia have different levels of MAO
It is thought that stress may increase susceptibility to illness through suppression of the immune system. In an experiment to investigate this theory, 48 rats were randomly allocated to four
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 three
An experiment was conducted in which the antiviral medication zanamivir was given to patients who had the flu. The length of time until the alleviation of major flu symptoms was measured for three
A researcher collected daffodils from four sides of a building and from an open area nearby. She wondered whether the average stem length of a daffodil depends on the side of the building on which it
A researcher studied the flexibility of 10 women in an aerobic exercise class, 10 women in a modern dance class, and a control group of 9 women. One measurement she made on each woman was spinal
The following computer output is for an analysis of variance in which yields (bu/acre) of different varieties of oats were compared.9(a) How many variety(groups) were in this experiment? (b) State
Consider using an F test to test the null hypothesis of equality of population means for the example data in the following graphs. For each pair of plots, identify which would yield the larger value
Radish seedlings were randomly distributed and then grown under four conditions: natural lighting, darkness, regular (incandescent) light bulb, and full spectrum light bulb (providing ultraviolet
Refer to the lymphocyte data of Exercise 11.4.2. The global F test is based on certain conditions concerning the population distributions. (a) State the conditions. (b) Which features of the data
Refer to the lymphocyte data of Exercise 11.4.2. (a) Suppose the lymphocyte concentration for one of the 12 rats in the mild stress group was 5.21. What is the value of the residual for this rat? (b)
Patients with advanced cancers of the stomach, bronchus, colon, ovary, or breast were treated with ascorbate. The purpose of the study was to determine if the survival times differ with respect to
Refer to the lymphocyte data of Exercise 11.4.2. (a) Looking at the summary data (means, SDs, ns) for the four groups, why might the conclusion of the ANOVA F test be questioned? (b) Despite the
In an experiment to compare six different fertilizers for tomatoes, 36 individually potted seedlings are to be used, 6 to receive each fertilizer. The tomato plants will be grown in a greenhouse, and
Consider the experiment described in Exercise I 1.6.8. In addition to measuring the number of mayfly nymphs at the end of 12 days, stones of the same size were removed from each channel, and the
In an experiment to investigate the effects of different soil nutrient amendments on pomegranate fruit yield (number of fruits per tree) researchers first selected 24 crop rows within a pomegranate
An experiment on vitamin supplements is to be conducted on young piglets, using litters as blocks in a randomized blocks design. There will be five treatments: four types of supplement and a control.
Refer to the vitamin experiment of Exercise 11.6.2. Suppose a colleague of the experimenter proposes an alternative design: All pigs in a given litter are to receive the same treatment, with the five
In a pharmacological experiment on eating behavior in rats, 18 rats are to be randomly allocated to three treatment groups: T1, T2, and T3 While under observation, the animals will be kept in
An experimenter is planning an agricultural field experiment to compare the yields of 25 varieties of corn. She will use a randomized blocks design with six blocks; thus, there will be 150 plots, and
For an experiment to compare two methods of artificial insemination in cattle, the following cows are available: Heifers (14-15 months old): 8 animals Young cows (2-3 years old): 8 animals Mature
True or false (and say why): The primary reason for using a randomized blocks design in an experiment is to reduce bias.
In an experiment to understand the impact of fish grazing on invertebrate populations in streams, researchers established nine observation channels in three streams (three channels per stream). Each
(a) The accompanying table is an (improper) ANOVA table for the data in Exercise 11.6.8. This analysis does not account for the blocking that was performed in the experiment. Based on this analysis,
A plant physiologist investigated the effect of flooding on root metabolism in two tree species: flood-tolerant river birch and the intolerant European birch. Four seedlings of each species were
Consider the data from Exercise 11.7.1. For these data, SS(species of birch) = 2.19781, SS(flooding) = 2.25751, SS(interaction) = 0.097656, and SS(within) = 0.47438. (a) Construct the ANOVA
A completely randomized double-blind clinical trial was conducted to compare two drugs, ticrynafen (T) and hydrochlorothiazide (H), for effectiveness in treatment of high blood pressure. Each drug
Consider the data from Exercise 11.7.3.The difference in response between T and H appears to be larger for the low dose than for the high dose. (a) Carry out an F test for interactions to assess
Consider the data from Exercise 11.7.3. For these data, SS(drug) = 69.22, SS(dose) = 330.00, SS(interaction) = 31.33, and SS(within) = 30648.81. (a) Construct the ANOVA table. (b) What is the value
In a study of lettuce growth. 36 seedlings were randomly allocated to receive either high or low light and to be grown in either a standard nutrient solution or one containing extra nitrogen. After
Patients with pleural infections (fluid buildup in the chest) were randomly assigned to either placebo (n = 55), the treatment "tPA" (tissue plasminogen activator) (n = 52), the treatment "DNase"
Forced expiratory volume (FEV) is a measure of the rate of airflow (L/min) during one deep exhalation. For each of 75 students, FEV was measured three times, and those results were averaged to give a
A scientist recorded the weights of 2La malaria-vector mosquitoes and compared them to their counterpart 2L + mosquitoes. The table below shows summary values broken down by sex.26(a) Prepare an
Refer to the FVC data of Example 11.8.1. (a) Verify that the grand mean of all 481 FVC values is 4.56. (b) Taking into account the age distribution among the 481 subjects and the age distribution in
Consider the daffodil data of Exercise 11.4.5. (a) Define a contrast to compare the stem length for daffodils from the open area versus the average of the north, south, east and west sides of the
To see if there is any relationship between blood pressure and childbearing, researchers examined data from a large health survey. The following table shows the data on systolic blood pressure (mm
Refer to the ATP data of Exercise 11.7.1. The sample means and standard deviations are as follows:Define linear combinations (i.e., specify the multipliers) to measure each of the following: (a) The
(a) Use a t test to investigate whether flooding has the same effect in river birch and in European birch. Use a nondirectional alternative and let α = 0.05. (The pooled standard deviation is
(Onsider the null hypothesis that flooding has no effect on ATP level in river birch. This hypothesis could be tested in two ways: as a contrast (using the method of Section 11.8), or with a
Consider the data from Exercise 11.7.3 in which the drugs ticrynafen (T) and hydrochlorothiazide (H) were compared. The data are summarized in the following table. The pooled standard deviation is
Consider the lettuce growth experiment described in Exercise 11.7.6. The accompanying table shows the mean leaf dry weight (gm) of the nine plants in each treatment group. MS(within) from the ANOVA
Refer to the MAO data of Exercise 11.4.1.(a) Define a contrast to compare the MAO activity for patients with schizophrenia without paranoid features versus the average of the two types with paranoid
Are the brains of left-handed people anatomically different? To investigate this question, a neuroscientist conducted postmortem brain examinations in 42 people. Each person had been evaluated before
A botanist used a completely randomized design to allocate 45 individually potted eggplant plants to five different soil treatments. The observed variable was the total plant dry weight without roots
Repeat Exercise 11.9.1, but use Bonferroni intervals with aew = 0.05.In Exercise 11.9.1A botanist used a completely randomized design to allocate 45 individually potted eggplant plants to five
In a study of the dietary treatment of anemia in cattle, researchers randomly divided 144 cows into tour treatment groups. Group A was a control group, and groups B, C, and D received different
Consider the experiment and data in Exercise 11.9.3.The experiment wise 95% Tukey HSD intervals are displayed using the statistical software package R.(a) Using the preceding output to support your
Ten treatments were compared for their effect on the liver in mice.There were 13 animals in each treatment group. The ANOVA gave MS(within) = 0.5842. The mean liver weights are given in the
Consider the data from Example 11.2.1 on the weight gain of lambs. The MS(within) from the ANOVA for these data was 23.333. The sample mean of diet 2 was 15 and of diet 1 was 11. (a) Use the
As mentioned in this section, the Bonferroni procedure can be used in a variety of circumstances. Consider the plover nesting example from Section 10.5, which compares plover nest locations across 3
Exercise 10.5.1 presented the following problem: Patients with painful knee osteoarthritis were randomly assigned in a clinical trial to one of five treatments: glucosamine, chondroitin, both,
Consider the research described in Exercise 11.4.6 in which 10 women in an aerobic exercise class, 10 women in a modern dance class, and a control group of 9 women were studied. One measurement made
Repeat the test in Exercise 11.S.7 using Y' instead of Y, and compare with the results of Exercise 1 l.S.7.
Suppose a drug for treating high blood pressure is to be compared to a standard blood pressure drug in a study of humans. (a) Describe an experimental design for a study that makes use of blocking.
In a study of balloon angioplasty, patients with coronary artery disease were randomly assigned to one of four treatment groups: placebo, probucol (an experimental drug), multivitamins (a combination
Refer to Exercise U.S. 12. Define contrasts to measure each effect specified, and calculate the value of each contrast.(a) The effect of probucol in the absence of multivitamins(b) The effect of
Refer to Exercise 11.S.12. Construct a 95% confidence interval (αcw = 0.05) for the effect of probucol in the absence of multivitamins. That is, construct a 95% confidence interval for μprobucol -
Refer to Exercise 11.S.12. Assuming all possible comparisons of group means will be computed, use the Bonferroni method to construct a 95% confidence interval for the effect of probucol in the
Three college students collected several pill-bugs from a woodpile and used them in an experiment in which they measured the time, in seconds, that it took for a bug to move 6 inches within an
Mountain climbers often experience several symptoms when they reach high altitudes during their climbs. Researchers studied the effects of exposure to high altitude on human skeletal muscle tissue.
Consider the data from Exercise 11.S.17.(a) Complete the following ANOVA table.(b) What is the value of the F test statistic used for testing for interactions? (c) The F-value for the interactions F
In a study to examine the utility of using ammonia gas to sanitize animal feeds, researchers inoculated corn silage with a strain of Salmonella. Next, two petri dishes of 5 g of contaminated feed
Refer to Exercise 11.S.l. The F test is based on certain conditions concerning the population distributions.(a) State the conditions.(b) The following dotplots show the raw data. Based on these plots
A biologist measured the post-orbital carapace length (mm) for specimens of two species of crayfish: Rusty crawfish and Sanborn crawfish. Summary statistics are given below.44For these data, SS(Sex)
In a study of the eye disease retinitis pigmentosa (RP), 211 patients were classified into four groups according to the pattern of inheritance of their disease. Visual acuity (spherical refractive
Another approach to the data analysis is to use the eye, rather than the person, as the observational unit. For the 211 persons there were 422 measurements of refractive error: the accompanying table
In a study of the mutual effects of the air pollutants ozone and sulfur dioxide. Blue Lake snap beans were grown in open-top field chambers. Some chambers were fumigated repeatedly with sulfur
Consider the data from Exercise 11.S.5. For these data, SS(ozone) = 0.696, SS(sulfur) = 0.492, SS(interaction) = 0.166, and SS(within) = 0.275. (a) Prepare an interaction graph (like Figure
Refer to Exercise 11.S.5. Define contrasts to measure each effect specified, and calculate the value of each contrast.(a) The effect of sulfur dioxide in the absence of ozone(b) The effect of sulfur
For the snap-bean data, use a t test to test the null hypothesis of no interaction against the alternative that sulfur dioxide is more harmful in the presence of ozone than in its absence. Let α =
Refer to the snap-bean data of Exercise 11.S.5. Apply a reciprocal transformation to the data. That is, for each yield value Y, calculate Y" = 1/Y. (a) Calculate the ANOVA table for Y' and carry out
Consider the following plots.(i)(ii) (iii) (iv) Continue Next Page. (v) (a) Arrange the following plots in order of their correlations (from closest to -1 to closest to +1). (b) Arrange plots (ii-iv)
Cellular ability to regulate homeostasis is measured by basal Ca pump activity. Deregulation of calciumhomeostasis can trigger serious effects of cell functioning. Can maternal mercury exposure
For each of the following examples, explain whether or not it is reasonable to treat the sample correlation coefficient, r, as an estimate of a population correlation coefficient p. Briefly justify
For each of the following data sets, compute a 95% confidence interval for the population correlation coefficient. (a) The blood chemistry data from Exercise 12.2.3. (b) The cob weight data from
Consider the following data. (a) Plot the data. Does there appear to be a relationship between X and Y? Is it linear or nonlinear? Weak or strong? (b) Compute the sample correlation coefficient
In a study of natural variation in blood chemistry, blood specimens were obtained from 284 healthy people. The concentrations of urea and of uric acid were measured for each specimen, and the
Researchers measured the number of neurons in the CA1 region of the hippocampus in the brains of eight persons who had died of causes unrelated to brain function. They found that these data were
Consider the study design and summary data presented in Exercise 12.2.4 to examine the correlation between age and the number of neurons in the CA1 region of the hippocampus. (a) Can this study be
Twenty plots, each 10x4 meters, were randomly chosen in a large field of corn. For each plot, the plant density (number of plants in the plot) and the mean cob weight (gm of grain per cob) were
Laetisaric acid is a compound that holds promise for control of fungus diseases in crop plants. The accompanying data show the results of growing the fungus Pythiumultimum in various concentrations

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