Question;Running head: MODULE 7 EXERCISES1Module 7 ExercisesKamie BestGrand Canyon University: PSY-520: Graduate StatisticsAugust 27, 2014MODULE 7 EXERCISES2Chapter 15:4. When doing an experiment with many groups, what is the problem with doing t tests betweenall possible groups without any correction? Why does use of the analysis of variance avoid thatproblem?The problem with utilizing a t-test with many groups is that there is an increase in the probabilityof a Type I error occurring. Yet, when we use the analysis of variance (ANOVA) method, it isspecifically designed to be used when there are two or more groups. It allows researchers toevaluate the mean of the single hypothesis through an a-level and reduces the potential of a TypeI error occurring.8. What are the assumptions underlying the analysis of variance?10. Find Fcrit for the following situations:a. df(numerator) = 2, df(denominator) = 16,? = 0.05b. df(numerator) = 3, df(denominator) = 36,? = 0.05c. df(numerator) = 3, df(denominator) = 36,? = 0.01What happens to Fcrit as the degrees of freedom increase and alpha is held constant? Whathappens to Fcrit when the degrees of freedom are held constant and alpha is made more stringent?12. What are the variables that affect the power of the one-way analysis of variance technique?MODULE 7 EXERCISES313. For each of the variables identified in Question 12, state how power is affected if the variableis 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 differencein sugar content among the three leading brands of breakfast cereal (brands A, B, and C). Toassess the amount of sugar in the cereals, you randomly sample six packages of each brand andchemically determine their sugar content. The following grams of sugar were found:a. Using the conceptual equations of the one-way ANOVA, determine whether any of the brandsdiffer 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 todetermine which cereals are different in sugar content.d. Same as part c, but use the Scheff? test.e. Explain any differences between the results of part c and part d.MODULE 7 EXERCISES423. Assume you are employed by a consumer-products rating service and your assignment is toassess car batteries. For this part of your investigation, you want to determine whether there is adifference 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 batteriesfrom each manufacturer and run them through laboratory tests that allow you to determine theuseful life of each battery. The following are the results given in months of useful battery life:a. Use the analysis of variance with? = 0.05 to determine whether there is a difference amongthese 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.26. A university researcher knowledgeable in Chinese medicine conducted a study to determinewhether acupuncture can help reduce cocaine addiction. In this experiment, 18 cocaine addictswere randomly assigned to one of three groups of 6 addicts per group. One group received 10weeks of acupuncture treatment in which the acupuncture needles were inserted into points onMODULE 7 EXERCISES5the outer ear where stimulation is believed to be effective. Another group, a placebo group, hadacupuncture needles inserted into points on the ear believed not to be effective. The third groupreceived no acupuncture treatment, instead, addicts in this group received relaxation therapy. Allgroups also received counseling over the 10-week treatment period. The dependent variable wascraving for cocaine as measured by the number of cocaine urges experienced by each addict inthe last week of treatment. The following are the results.a. Using? =0.05, what do you conclude?b. If there is a significant effect, estimate the size of effect, usingc. This time estimate the size of the effect, using??.d. Explain the difference in answers between part b and part c..MODULE 7 EXERCISES6Chapter 16:11. It is theorized that repetition aids recall and that the learning of new material can interferewith the recall of previously learned material. A professor interested in human learning andmemory conducts a 2 X 3 factorial experiment to investigate the effects of these two variables onrecall. The material to be recalled consists of a list of 16 nonsense syllable pairs. The pairs arepresented one at a time, for 4 seconds, cycling through the entire list, before the first pair isshown 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, eachsubject 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 originallist of 16 nonsense syllable pairs. Thirty-six college freshmen serve as subjects. They arerandomly assigned so that there are six per cell. The following scores are recorded, each is thenumber of syllable pairs from the original list correctly recalled.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 theresults.12. Assume you have just accepted a position as chief scientist for a leading agriculturalcompany. Your first assignment is to make a recommendation concerning the best type of grassto grow in the Pacific Northwest and the best fertilizer for it. To provide the database for yourrecommendation, having just graduated summa cum laude in statistics, you decide to conduct anMODULE 7 EXERCISES7experiment involving a factorial independent groups design. Since there are three types of grassand two fertilizers under active consideration, the experiment you conduct is 2 X 3 factorial,where the A variable is the type of fertilizer and the B variable is the type of grass. In your fieldstation, you duplicate the soil and the climate of the Pacific Northwest. Then you divide the soilinto 30 equal areas and randomly set aside 5 for each combination of treatments. Next, youfertilize 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 thenumber of grass blades per square inch in each area. Your recommendation is based on thisdependent variable. The ?denser? the grass is, the better. The following scores are obtained: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 youinterpret the results.13. A sleep researcher conducts an experiment to determine whether a hypnotic drug calledDrowson, 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. Thedesign of the experiment is a 2 X 2 factorial independent groups design. One of the variables isthe concentration of Drowson. There are two levels: (1) zero concentration (placebo) and (2) themanufacturer?s minimum recommended dosage. The other variable oncerns the previous use ofDrowson. 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 noprevious use of Drowson are randomly assigned to the two concentration conditions, such thatthere are eight subjects in each condition. Sixteen chronic users of Drowson are also assignedrandomly 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 shownMODULE 7 EXERCISES8in the following table are the mean times in minutes to fall asleep for each subject, averaged overthe 3 days: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 theresults.ReferencesMODULE 7 EXERCISES9Academic Web Services (n.d.). The Visual Learner ? Statistics. Retrieved from:http://lc.gcumedia.com/zwebassets/courseMaterialPages/psy520_the-visual-learnerv1.1.php.Pagano, R. (2013). Understanding Statistics in the Behavioral Sciences (10th ed.). WadsworthCengage Learning.
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