STAT200 WK6 complete solutions correct answers key

STAT200 WK6 complete solutions correct answers key

DIS #1

In the North American court system, a defendant is assumed innocent until proven guilty.  In an ideal world, we would expect that the truly innocent will always go free, whereas the truly guilty ones will always be convicted.  Now, let us tackle the following questions?

In the context of the Type I error and Type II error, can you relate a court trial scenario in terms of these two errors?

What would be your ideal situation if you are the defendant?

What would be your ideal situation if you are the prosecuting attorney?

As jurors we must feel that the evidence presented justifies our decision (innocent or guilty) BEYOND a reasonable doubt.  Is this ever possible, statistically speaking? 

Nowadays with “trials” by media, can we get an truly unbiased jury?  As a “lawyer” how might you counter that issue?

TERMPRO #6

WITH THE DATA BELOW FOR (QUARTERS) TOSSED 30 TIMES: come up with a null hypothesis (Ho) and an alternate hypothesis.  Make it a one or two tailed test as you like.  Then, test for it using the z or t-test (with or without the population standard deviation), calculate the test statistic, IDENTIFY the critical z or t value for the significance level you chose (1%, 5% or 10%) and test the hypothesis ?  (You should already have the critical values for these 3 percentages).  Did you accept or reject Ho ?  Why?  Explain this conclusion in your own words.

2.5

3

5.25

5.5

7

8

9.25

9.75

9.75

10.5

11

11.5

12

12

13

13.5

14.5

17.5

19.5

21

22

22

23.5

28.5

29.5

29.5

31

33.25

34

46

HW:

NON-TEXT PROBLEM #1 :  What are the CRITICAL  z-values that correspond to alphas of 1%, 5% and 10% for the LEFT TAIL and the RIGHT TAIL  (6 numbers required)?  Now, split the alphas between both ends and give those pairs of values (right and left tails) for the these α /2  (again, 6 numbers required).  That’s it for this question.

LANE (CHAPTER 11) PROBLEM #4

State the null hypothesis for: a. An experiment testing whether echinacea decreases the length of colds. b. A correlational study on the relationship between brain size and intelligence. c. An investigation of whether a self-proclaimed psychic can predict the outcome of a coin flip. d. A study comparing a drug with a placebo on the amount of pain relief. (A onetailed test was used.)

LANE (CHAPTER 11) PROBLEMS #18 - #24

18. You choose an alpha level of .01 and then analyze your data.

a. What is the probability that you will make a Type I error given that the null hypothesis is true?

b. What is the probability that you will make a Type I error given that the null hypothesis is false?

19. Why doesn’t it make sense to test the hypothesis that the sample mean is 42?

20. True/false: It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level.

21. True/false: You are more likely to make a Type I error when using a small sample than when using a large sample.

22. . True/false: You accept the alternative hypothesis when you reject the null hypothesis.

23. True/false: You do not accept the null hypothesis when you fail to reject it.

24. True/false: A researcher risks making a Type I error any time the null hypothesis is rejected.

LANE (CHAPTER 12)  PROBLEM #13

You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The first group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100.

a. What is the calculated t value? Are the mean test scores of these two groups significantly different at the .05 level?

b. What would the t value be if there were only 6 participants in each group? Would the scores be significant at the .05 level?

LANE (CHAPTER 13)  PROBLEMS #1 AND #2 

1. Define power in your own words.

2. List 3 measures one can take to increase the power of an experiment. Explain why your measures result in greater power.

ILLOWSKY CHAPTER 9

ILLOWSKY (CHAPTER 9) PROBLEM #77

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

ILLOWSKY (CHAPTER 10) PROBLEM # 80

At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Relaxed time (seconds) Jumping time (seconds)

26 21

47 40

30 28

22 21

23 25

45 43

37 35

29 32

PROBLEM #87

The exact distribution for the hypothesis test is:

a. the normal distribution

b. the Student's t-distribution

c. the uniform distribution

d. the exponential distribution