Project #27892 - statistic

1.             Explain in your own words why it is important to know the possible errors we might make when rejecting or failing to reject the null hypothesis.

With Type I error, the null hypothesis is true so we reject it. When the null hypothesis is false this is considered a type ii error so we fail to reject the null hypothesis.

 

9. A primatologist believes that rhesus monkeys possess curiosity. She reasons that, if this is true, then they should prefer novel stimulation to repetitive stimulation. An experiment is conducted in which 12 rhesus monkeys are randomly selected from the university colony and taught to press two bars. Pressing bar 1 always produces the same sound, whereas bar 2 produces a novel sound each time it is pressed. After learning to press the bars, the monkeys are tested for 15 minutes, during which they have free access to both bars. The number of presses on each bar during the 15 minutes is recorded.

 The resulting data are as follows:

Subject Bar 1 Bar 2

1 20 40

2 18 25

3 24 38

4 14 27

5 5 31

6 26 21

7 15 32

8 29 38

9 15 25

10 9 18

11 25 32

12 31 28

a.     What is the alternative hypothesis? In this case, assume a non directional hypothesis is appropriate because there is insufficient empirical basis to warrant a directional hypothesis.

The Alternative Hypothesis is Rhesus Monkeys do not prefer novel stimulation (Bar 2) to repetitive stimulation (Bar 1)

b.     What is the null hypothesis?

       The Null Hypothesis is Rhesus Monkeys prefer novel stimulation (Bar 2) to repetitive stimulation (Bar 1)

 

c. Using _ _ 0.052 tail, what is your conclusion?

d. What error might you be making by your conclusion in part c?

e. To what population does your conclusion apply?

 

13. A researcher is interested in determining whether acupuncture affects pain tolerance. An experiment is performed in which 15 students are randomly chosen from a large pool of university undergraduate volunteers. Each subject serves in two conditions. In both conditions, each subject receives a short-duration electric shock to the pulp of a tooth. The shock intensity is set to produce a moderate level of pain to the unanesthetized subject. After the shock is terminated, each subject rates the perceived level of pain on a scale of 0–10, with 10 being the highest level. In the experimental condition, each subject receives the appropriate acupuncture treatment prior to receiving the shock. The control condition is made as similar to the experimental condition as possible, except a placebo treatment is given instead of acupuncture. The two conditions are run on separate days at the same time of day. The pain ratings in the accompanying table are obtained.

a. What is the alternative hypothesis? Assume a nondirectional hypothesis is appropriate.

b. What is the null hypothesis?

c. Using _ _ 0.052 tail, what is your conclusion?

d. What error might you be making by your conclusion in part c?

e. To what population does your conclusion apply?

 

Subject Acupuncture Placebo

1 4 6

2 2 5

3 1 5

4 5 3

5 3 6

6 2 4

7 3 7

8 2 6

9 1 8

10 4 3

11 3 7

12 4 8

13 5 3

14 2 5

15 1 4

2.            Chapter 12, # 3, 5, 8, 16, 20, 21, 25

3. How are sampling distributions generated using the empirical sampling approach?

 

5.             What are the assumptions underlying the use of the z test?

 

8. How do each of the following differ?

a. s and sX

b. s2 and _2

c. _ and _X

d. _ and _X

 

16. How does increasing the N of an experiment affect the following?

a. Power

b. Beta

c. Alpha

d. Size of real effect

 

20. A set of sample scores from an experiment has an N _ 30 and an Xobt _ 19.

a. Can we reject the null hypothesis that the sample is a random sample from a normal population with _ _ 22 and _ _ 8? Use _ _ 0.011 tail. Assume the sample mean is in the correct direction.

b. What is the power of the experiment to detect a real effect such that _real _ 20?

c. What is the power to detect a _real _ 20 if N is increased to 100?

d. What value does N have to equal to achieve a power of 0.8000 to detect a μreal _ 20? Use the nearest table value for zobt. other

 

21. On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution. As director of training at a nearby institution, you agree to let her try her method on 20 schizophrenics, randomly sampled from your institution. The mean duration that schizophrenics stay at your institution is 85 weeks, with a standard deviation of 15 weeks. The scores are normally distributed. The results of the experiment show that the patients treated by the student stay a mean duration of 78 weeks, with a standard deviation of 20 weeks.

a. What is the alternative hypothesis? In this case, assume a nondirectional hypothesis is appropriate because there are insufficient theoretical and empirical bases to warrant a directional hypothesis.

b. What is the null hypothesis?

c. What do you conclude about the student’s technique? Use _ _ 0.052 tail. clinical, health

 

25. A physical education professor believes that exercise can slow the aging process. For the past 10 years, he has been conducting an exercise class for 14 individuals who are currently 50 years old. Normally, as one ages, maximum oxygen consumption decreases. The national norm for maximum oxygen consumption in 50-year-old individuals is 30 milliliters per kilogram per minute, with a standard deviation of 8.6. The mean of the 14 individuals is 40 milliliters per kilogram per minute. What do you conclude? Use _ _ 0.051 tail.

 

1.    Chapter Thirteen # 3, 12, 14, 20

2.     Elaborate on what is meant by degrees of freedom. Use an example.

 

A sample set of 29 scores has a mean of 76 and a standard deviation of 7. Can we accept the hypothesis that the sample is a random sample from a population with a mean greater than 72? Use _ _ 0.011 tail in making your decision. Other

 

Using each of the following random samples, determine the 95% and 99% confidence intervals for the population mean:

a. Xobt _ 25, s _ 6, N _ 15

b. Xobt _ 120, s _ 8, N _ 30

c. Xobt _ 30.6, s _ 5.5, N _ 24

d. Redo part a with N _ 30. What happens to the confidence interval as N increases? Other

 

20. A physician employed by a large corporation believes that due to an increase in sedentary life in the past decade, middle-age men have become fatter. In 1995, the corporation measured the percentage of fat in their employees. For the middle-age men, the scores were normally distributed, with a mean of 22%. To test her hypothesis, the physician measures the fat percentage in a random sample of 12 middle-age men currently employed by the corporation. The fat percentages found were as follows: 24, 40, 29, 32, 33,

25, 15, 22, 18, 25, 16, 27. On the basis of these data, can we conclude that middle-age men employed by the corporation have become fatter? Assume a directional

H1 is legitimate and use _ _ 0.051 tail in making your decision. health

3.    Chapter Fourteen # 14, 17, 23

4.     14. You are interested in determining whether an experimental birth control pill has the side effect of changing blood pressure. You randomly sample ten women from the city in which you live. You give five of them a placebo for a month and then measure their diastolic blood pressure. Then you switch them to the birth control pill for a month and again measure their blood pressure. The other

 

5.     17. The manager of the cosmetics section of a large department store wants to determine whether newspaper advertising really does affect sales. For her experiment, she randomly selects 15 items currently in stock and proceeds to establish a baseline. The 15 items are priced at their usual competitive values, and the quantity of each item sold for a 1-week period is recorded. Then, without changing their price, she places a large ad in the newspaper, advertising he 15 items. Again, she records the quantity sold for a 1-week period. The results follow.

Item

No. Sold

Before Ad

No. Sold

After Ad

1 25 32

2 18 24

3 3 7

4 42 40

5 16 19

6 20 25

7 23 23

8 32 35

9 60 65

10 40 43

11 27 28

12 7 11

13 13 12

14 23 32

15 16 28

 

a. Using _ _ 0.052 tail, what do you conclude?

b. What is the size of the effect? I/O

 

23. An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in this experiment. One member of each twin pair is enrolled in preschool for 2 years while the other member of each pair remains at home. At the end of the 2 years, the IQs of all the children are measured. The results follow.

IQ

Pair

Twin at

preschool

Twin at

home

1 110 114

2 121 118

3 107 103

4 117 112

5 115 117

6 112 106

7 130 125

8 116 113

9 111 109

10 120 122

11 117 116

12 106 104

Does early exposure to school affect IQ? Use_ _ 0.052 tail.

 

 

Subject Mathematics
Due By (Pacific Time) 04/16/2014 08:00 pm
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