# 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

CHAPTER 15

(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

variance?

(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

(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

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 _ _ 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

A B C

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;

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 _ _ 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

CHAPTER 16

(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)

Intervening

Material (row

variable)

4

times

8

times

12

times

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

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:

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 _ _ 0.05, what are your conclusions? Draw

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

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 _ _ 0.05, what do you conclude? Plot a

results. clinical, health

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