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

 

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

 

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;

 

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 _ _ 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

 

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

 

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

 

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

 

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

 

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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