**Show all workings and complete in Microsoft Word only.**

1. 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?

2. What are the assumptions underlying the analysis of variance?

3. Find *F*crit for the following situations:

a. df(numerator) =2, df(denominator) =16, *α *= 0.05

b. df(numerator) =3, df(denominator) =36, *α *= 0.05

c. df(numerator) =3, df(denominator) =36, *α*= 0.01

What happens to *F*crit as the degrees of freedom increase and alpha is held constant? What happens

to *F*crit when the degrees of freedom are held constant and alpha is made more stringent?

4. 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.

5. 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**

**A B C**

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 *α *= 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 *α *= 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**.

6. 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**

*A B C*

56 46 44

57 52 53

55 51 50

59 50 51

a. Use the analysis of variance with *α *=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 *α *=0.05 to help you with your decision.

7. 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 **+**Counseling** **Placebo **+**Counseling ** **Relaxation Therapy **+**Counseling**

4 8 12

7 12 7

6 11 9

5 8 6

2 10 11

3 7 6

a. Using *α *= 0.05, what do you conclude?

b. If there is a significant effect, estimate the size of effect, using Åµ2.

c. This time estimate the size of the effect, using *η²*.

d. Explain the difference in answers between part **b **and part **c**.

8. 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 first 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 of16 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)**

** **

**Intervening**

**Material (row 4 times 8 times 12 times**

**variable)***4*

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 *α *=0.05, what do you conclude? Plot a graph of the cell means to help you interpret the results.

9. 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 x 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**

**Fertilizer**

* **Red Fescue Kentucky Blue Green Velvet*

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 *α*=0.05, what are your conclusions? Draw a graph of the cell means to help you interpret the results.

10. 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 Minimum Recommended Dosage*

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 *α *= 0.05, what do you conclude? Plot a graph of the cell means to help you interpret the

results.

11. A study was conducted to determine whether big-city and small-town dwellers differed in their helpfulness to strangers. In this study, the investigators rang the doorbells of strangers living in New York City or small towns in the vicinity. They explained they had misplaced the address of a friend living in the neighborhood and asked to use the phone. The following data show the number of individuals who admitted or did not admit the strangers (the investigators) into their homes:

**Helpfulness to Strangers**

* **Admitted strangers Did not admit strangers *

into their home into their home

Big-city dweller 60 90 150

Small-town dweller 70 30 100

130 120 250

Do big-city dwellers differ in their helpfulness to strangers? Use *α *= 0.05 in making your decision.

12. A researcher believes that individuals in different occupations will show differences in their ability

to be hypnotized. Six lawyers, six physicians, and six professional dancers are randomly selected for the experiment. A test of hypnotic susceptibility is administered to each. The results are shown in

the next column. The higher the score, the higher the hypnotizability. Assume the data violate the assumptions required for use of the *F *test, but are at least of ordinal scaling. Using *α *= 0.05, what is your conclusion?

**Condition 1 Lawyers Condition 2 Physicians Condition 3 Dancers**

26 14 30

17 19 21

27 28 35

32 22 29

20 25 37

25 15 34

13. A psychologist investigates the hypothesis that birth order affects assertiveness. Her subjects are 20 young adults between 20 and 25 years of age. There are seven first-born, six second-born, and seven third born subjects. Each subject is given an assertiveness test, with the following results. High scores indicate greater assertiveness. Assume the data are so far from normally distributed that the *F *test can’t be used, but the data are at least of ordinal scaling. Use *α *= 0.01 to evaluate the data. What is your conclusion?

**Condition 1 First-Born Condition 2 Second-Born Condition 3 Third-Born**

18 18 7

8 12 19

4 3 2

21 24 30

28 22 18

32 1 5

10 14

14. A major oil company conducts an experiment to assess whether a fi lm designed to tell the truth

about, and also promote more favorable attitudes toward, large oil companies really does result in more favorable attitudes. Twelve individuals are run in a replicated measures design. In the “Before” condition, each subject fills out a questionnaire designed to assess attitudes toward large oil companies. In the “After” condition, the subjects see the fi lm, after which they fill out the questionnaire. The following scores were obtained. High scores indicate more favorable attitudes toward large oil companies.

** **

**Before After**

43 45

48 60

25 22

24 33

15 7

18 22

35 41

28 21

41 55

28 33

34 44

12 23

Analyze the data using the Wilcoxon signed ranks test with *α *=0.051 tail. What do you conclude?

15. A social scientist believes that university theology professors are more conservative in political

orientation than their colleagues in psychology. A random sample of 8 professors from the theology department and 12 professors from the psychology department at a local university are given a 50-point questionnaire that measures the degree of political conservatism. The following scores were obtained. Higher scores indicate greater conservatism.

a. What is the alternative hypothesis? In this case, assume a non-directional hypothesis is appropriate

because there are insufficient theoretical and empirical bases to warrant a directional hypothesis.

b. What is the null hypothesis?

c. What is your conclusion? Use the Mann–Whitney *U *test and *α =*0.052 tail.

** **

** **

**Theology Professors Psychology Professors**

36 13

42 25

22 40

48 29

31 10

35 26

47 43

38 17

12

32

27

32

Subject | Mathematics |

Due By (Pacific Time) | 12/03/2014 08:00 am |

Tutor | Rating |
---|---|

pallavi Chat Now! |
out of 1971 reviews More.. |

amosmm Chat Now! |
out of 766 reviews More.. |

PhyzKyd Chat Now! |
out of 1164 reviews More.. |

rajdeep77 Chat Now! |
out of 721 reviews More.. |

sctys Chat Now! |
out of 1600 reviews More.. |

sharadgreen Chat Now! |
out of 770 reviews More.. |

topnotcher Chat Now! |
out of 766 reviews More.. |

XXXIAO Chat Now! |
out of 680 reviews More.. |