Project #31875 - Statistics


Complete the following exercises from "Questions and Problems" located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.


1. Chapter 15, # 4, 8, 10, 13, 20, 23, 26


2. Chapter 16, # 11, 12, 13






(4). When doing an experiment with many groups, what


is the problem with doing t tests between all possible


groups without any correction? Why does use of the


analysis of variance avoid that problem?


(8). What are the assumptions underlying the analysis of




(10). Find Fcrit for the following situations:


a. df(numerator) _ 2, df(denominator) _ 16, _ _ 0.05


b. df(numerator) _ 3, df(denominator) _ 36, _ _ 0.05


c. df(numerator) _ 3, df(denominator) _ 36, _ _ 0.01


What happens to Fcrit as the degrees of freedom


increase and alpha is held constant? What happens


to Fcrit when the degrees of freedom are held constant


and alpha is made more stringent?


(13). For each of the variables identified in Question 12,


state how power is affected if the variable is increased.


Use the equation for Fobt on p. 421 to justify


your answer.


(20). Assume you are a nutritionist who has been asked


to determine whether there is a difference in sugar


content among the three leading brands of breakfast


cereal (brands A, B, and C). To assess the amount


of sugar in the cereals, you randomly sample six


packages of each brand and chemically determine


their sugar content. The following grams of sugar


were found:


Breakfast Cereal




1 7 6


2 5 4


3 3 4


3 7 5


2 4 7


6 7 8


a. Using the conceptual equations of the one-way


ANOVA, determine whether any of the brands differ


in sugar content. Use _ _ 0.05.


b. Same as part a, except use the computational equations.


Which do you prefer? Why?


c. Do a post hoc analysis on each pair of means using


the Tukey HSD test with _ _ 0.05 to determine which


cereals are different in sugar content.


d. Same as part c, but use the Scheffe test.


e. Explain any differences between the results of part c


and part d. health


(23). Assume you are employed by a consumer-products


rating service and your assignment is to assess car


batteries. For this part of your investigation, you


want to determine whether there is a difference in


useful life among the top-of-the-line car batteries


produced by three manufacturers (A, B, and C). To


provide the database for your assessment, you randomly


sample four batteries from each manufacturer


and run them through laboratory tests that allow


you to determine the useful life of each battery. The


following are the results given in months of useful


battery life:


Battery Manufacturer




56 46 44


57 52 53


55 51 50


59 50 51


USE the analysis of variance with _ _ 0.05 to determine


whether there is a difference among these three


brands of batteries.


b. Suppose you are asked to make a recommendation


regarding the batteries based on useful life. Use the


Tukey HSD test with _ _ 0.05 to help you with your


decision. I/O


26. A university researcher knowledgeable in Chinese


medicine conducted a study to determine whether


acupuncture can help reduce cocaine addiction. In


this experiment, 18 cocaine addicts were randomly


assigned to one of three groups of 6 addicts per


group. One group received 10 weeks of acupuncture


treatment in which the acupuncture needles were


inserted into points on the outer ear where stimulation


is believed to be effective. Another group, a


placebo group, had acupuncture needles inserted


into points on the ear believed not to be effective.


The third group received no acupuncture treatment;


instead, addicts in this group received relaxation


therapy. All groups also received counseling over the


10-week treatment period. The dependent variable


was craving for cocaine as measured by the number


of cocaine urges experienced by each addict in the


last week of treatment. The following are the results.


Acupuncture _




Placebo _




Relaxation Therapy _




4 8 12


7 12 7


6 11 9


5 8 6


2 10 11


3 7 6


a. Using _ _ 0.05, what do you conclude?


b. If there is a significant effect, estimate the size of


effect, using _ˆ 2.


c. This time estimate the size of the effect, using _2.


d. Explain the difference in answers between part b and


part c. clinical, health


27. An instructor is teaching




(11). It is theorized that repetition aids recall and that the


learning of new material can interfere with the recall


of previously learned material. A professor interested


in human learning and memory conducts a 2 _ 3 factorial


experiment to investigate the effects of these


two variables on recall. The material to be recalled


consists of a list of 16 nonsense syllable pairs. The


pairs are presented one at a time, for 4 seconds,


cycling through the entire list, before the fi rst pair


is shown again. There are three levels of repetition:


level 1, in which each pair is shown 4 times; level 2,


in which each pair is shown 8 times; and level 3, in


which each pair is shown 12 times. After being presented


the list the requisite number of times and prior


to testing for recall, each subject is required to learn


some intervening material. The intervening material is


of two types: type 1, which consists of number pairs,


and type 2, which consists of nonsense syllable pairs.


After the intervening material has been presented,


the subjects are tested for recall of the original list of


16 nonsense syllable pairs. Thirty-six college freshmen


serve as subjects. They are randomly assigned so


that there are six per cell. The following scores are


recorded; each is the number of syllable pairs from the


original list correctly recalled.


Number of Repetitions


(column variable)




Material (row
















Number pairs 10 11 16 12 16 14


12 15 11 15 16 13


14 10 13 14 15 16


Nonsense 8 7 11 13 14 12


syllable pairs 4 5 9 10 16 15


5 6 8 9 12 13


a. What are the null hypotheses for this experiment?


b. Using _ _ 0.05, what do you conclude? Plot a


graph of the cell means to help you interpret the


results. cognitive




(12). Assume you have just accepted a position as chief


scientist for a leading agricultural company. Your


first assignment is to make a recommendation concerning


the best type of grass to grow in the Pacific


Northwest and the best fertilizer for it. To provide


the database for your recommendation, having just


graduated summa cum laude in statistics, you decide


to conduct an experiment involving a factorial independent


groups design. Since there are three types


of grass and two fertilizers under active consideration,


the experiment you conduct is 2 _ 3 factorial,


where the A variable is the type of fertilizer and the


B variable is the type of grass. In your field station,


you duplicate the soil and the climate of the Pacific


Northwest. Then you divide the soil into 30 equal


areas and randomly set aside 5 for each combination


of treatments. Next, you fertilize the areas with


the appropriate fertilizer and plant in each area the


appropriate grass seed. Thereafter, all areas are


treated alike. When the grass has grown sufficiently,


you determine the number of grass blades per square


inch in each area. Your recommendation is based on


this dependent variable. The “denser” the grass is,


the better. The following scores are obtained:


Number of Grass Blades


Per Square Inch
















Type 1 14 15 15 17 20 19


16 17 12 18 15 22


10 11 25


Type 2 11 7 10 6 15 11


11 8 8 13 18 10


14 12 19


a. What are the null hypotheses for this experiment?


b. Using _ _ 0.05, what are your conclusions? Draw


a graph of the cell means to help you interpret the


results. I/O




(13). A sleep researcher conducts an experiment to determine


whether a hypnotic drug called Drowson,


which is advertised as a remedy for insomnia, actually


does promote sleep. In addition, the researcher


is interested in whether a tolerance to the drug


develops with chronic use. The design of the experiment


is a 2 _ 2 factorial independent groups


design. One of the variables is the concentration


of Drowson. There are two levels: (1) zero concentration


(placebo) and (2) the manufacturer’s minimum


recommended dosage. The other variable


concerns the previous use of Drowson. Again there


are two levels: (1) subjects with no previous use and


(2) chronic users. Sixteen individuals with sleep onset


insomnia (difficulty in falling asleep) who


have had no previous use of Drowson are randomly


assigned to the two concentration conditions, such


that there are eight subjects in each condition.


Sixteen chronic users of Drowson are also assigned


randomly to the two conditions, eight subjects


per condition. All subjects take their prescribed


“medication” for 3 consecutive nights, and the


time to fall asleep is recorded. The scores shown in


the following table are the mean times in minutes


to fall asleep for each subject, averaged over the


3 days:


Concentration of Drowson


Previous Use Placebo








No previous use 45 53 30 47


48 58 33 35


62 55 40 31


70 64 50 39


Chronic users 47 68 52 46


52 64 60 49


55 58 58 50


62 59 68 55


a. What are the null hypotheses for this experiment?


b. Using _ _ 0.05, what do you conclude? Plot a


graph of the cell means to help you interpret the


results. clinical, health








Subject Mathematics
Due By (Pacific Time) 05/29/2014 12:00 am
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