Scenario 1: Use the following for problems 1 though 6. There are a number of things that are related to the cost of coffee; such as consumer demand, governmental support of coffee growers, climatic conditions, etc. In this problem we are only going to be concerned about the amount of rainfall during the harvesting season; specifically is the amount of rainfall related to the cost of coffee. Our two variables of interest are Rain - number of inches of rain during the harvesting season Cost - cost (cents) per pound of coffee that the grower gets Here are the data from 15 different regions in Columbia.
Region of Columbia
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Rain .50 .50 1.00 .25 .00 .75 1.25 1.00 .00 1.25 .75 1.50 .25 .50 .75
Cost 51 43 57 55 43 46 58 48 45 60 58 59 42 49 51
Here might be some helpful information.
Rain Variable Cost Variable
Mean = .683 Mean = 51.0
Variance = .210 Variance = 41.3
Sum (values - mean)2 = 2.933 Sum (values - mean)2 = 578.0
Covariance of Rain and Cost = 2.16 Correlation of Rain and Cost = .73 2p S = 20.76
1. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
2. What is the appropriate alternative hypothesis for this scenario?
a. The amount of rain is not related to the cost of the coffee.
b. The amount of rain is related to the cost of the coffee.
c. The amount of rain is correlated with the cost of the coffee.
d. The amount of rain is not correlated with the cost of the coffee.
e. Both a. and d.
f. Both b. and c.
g. None of the above
3. Given the numerical information above, what is the value of r? __________
4. What is (are) the critical value(s) for this scenario?
a. - 2.160 b. 2.160 c. +/- 2.048 d. +/- 2.160 e. +/- 2.131 f. +/- 2.145
5. If the results were determined to be significant, which of the conclusions below is correct?
a. The amount of rain is related to the cost of the coffee.
b. The amount of rain is not related to the cost of the coffee.
c. Higher amounts of rain are related to higher coffee prices.
d. Higher amounts of rain are related to lower coffee prices.
e. Reject H0
f. Fail to Reject H0
g. None of the above
6. If the results were determined to be insignificant, which of the conclusions below is correct?
a. The amount of rain is related to the cost of the coffee.
b. The amount of rain is not related to the cost of the coffee.
c. Higher amounts of rain are related to higher coffee prices.
d. Higher amounts of rain are related to lower coffee prices.
e. Reject H0
f. Fail to Reject H0
g. None of the above
Scenario 2: Use the following for problems 7 through 11. One of the most significant changes in American moving making in the past 10 years is the tremendous increase in movies which either have Zombies or Vampires as the central theme. Ten years ago half of all Americans believed that vampires actually exist. My question is "do more Americans believe that vampires actually exist than 10 years ago?" To address this question, I asked 100 adult citizens of the United States "Do you believe that vampires actually exist: Yes or No?" Here are the results for the outcome of interest: Yes (f = 57).
7. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
8. In the context of this scenario, which of the following is the most appropriate HA?
a. Vampires exist
b. More vampires exist today than did 10 years ago
c. Vampires exist or they don't
d. More than half of all Americans believe that vampires exist
e. The same proportion of Americans believe vampires exist as don't
9. What is the value of the critical value?
a. - 1.645 b. 1.645 c. ±1.645 d. 1.96 e. ±.05
10. What is the value of the test statistic? (round off to 2 decimal places) __________
11. For this problem only, if TS < CV, then which of the following statistical decisions and conclusions is most
appropriate?
a. Fail to Reject H0, more than half of all Americans believe that vampires exist
b. Fail to Reject H0, the same proportion of Americans believe vampires exist as don't
c. Fail to Reject H0, a different proportion of Americans believe vampires exist as don't
d. Reject H0, more than half of all Americans believe that vampires exist
e. Reject H0, the same proportion of Americans believe vampires exist as don't
f. Reject H0, a different proportion of Americans believe vampires exist as don't
Scenario 3: Use the following for problems 12 though 16. Do people who have served in the military have a similar or different opinion than people who haven't served in the military about our military presence in Afghanistan? To answer this question I asked a sample of 100 people who have served in the military and a sample of 100 people who haven't served in the military the following, "do you believe that we need to continue to have a military presence in Afghanistan: Yes, No?
Continued Presence in Afghanistan
Yes No
12. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
13. In the context of this scenario, which of the following is the most appropriate HA?
a. Having served in Afghanistan is related to belief in a continued military presence in Afghanistan
b. Having served in Afghanistan is not related to belief in a continued military presence in Afghanistan
c. Those who have served in the military will have a similar opinion about a continued military presence in Afghanistan as those who haven't served in the military.
d. Those who have served in the military will not have a similar opinion about a continued military presence in Afghanistan as those who haven't served in the military.
14. What is the value of the critical value? __________
15. What is the value of the test statistic? (round off to 2 decimal places) __________
16. For this problem only, if TS > CV, then which of the following conclusions is most appropriate?
a. Fail to Reject H0
b. Reject H0
c. Those who have served in the military will have a similar opinion about a continued military presence in Afghanistan as those who haven't served in the military.
d. Those who have served in the military will not have a similar opinion about a continued military presence in Afghanistan as those who haven't served in the military.
e. Those who have served in the military are more likely believe to that we should not continue to have a continued military presence in Afghanistan and that those who haven't served in the military are more likely to believe that we should continue to have a continued military presence in Afghanistan.
Have Served
20
80
Haven't Served
70
30
5
Scenario 4: Use the following for problems 17 though 21. Do freshmen or seniors have more fun? To answer this question, I asked a random sample of 13 freshmen and a random sample of 12 seniors, "What percent of the past academic year has been fun: 0 = 0%, 1 = 10%, 2 = 20%, 3 = 30%, ... , 9 = 90%, or 10 = 100%?" Here are the results
Sample Mean
Freshmen 6.1
Seniors 7.7
17. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
18. In the context of this scenario, which of the following is the most appropriate H0?
a. Senior and freshmen have the same amount of fun
b. Senior and freshmen don't have the same amount of fun
c. Seniors have more fun than freshmen
d. Seniors have less fun than freshmen
e. More seniors have fun than freshmen
19. In the context of this scenario, which of the following is the most appropriate HA?
a. Senior and freshmen have the same amount of fun
b. Senior and freshmen don't have the same amount of fun
c. Seniors have more fun than freshmen
d. Seniors have less fun than freshmen
e. More seniors have fun than freshmen
20. Calculate the value of δ. __________
21. If the statistical decision was to Reject H0, then which of the following is the most appropriate conclusion?
a. Senior and freshmen have the same amount of fun
b. Senior and freshmen don't have the same amount of fun
c. Seniors have more fun than freshmen
d. Seniors have less fun than freshmen
e. More seniors have fun than freshmen
Scenario 5: Use the following for problems 22 though 26. Do women feel pressure at work to follow an implied dress code? To investigate this question, I asked a sample of 120 professional women within the same company in Denver the following question, "Do you feel pressured to follow an implied dress code at work: Not at All, Sometimes, or Definitely?"
Pressured
Not at All Sometimes Definitely
22. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
23. In the context of this scenario, which of the following is the most appropriate HA?
a. Women definitely feel pressured at work to follow an implied dress code
b. Women feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
c. Women don't feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
d. Do women feel pressured at work to follow an implied dress code
24. What is the value of the critical value? __________
25. What is the value of the test statistic? (round off to 2 decimal places) __________
26. For this problem only, if the value of the TS > the value of the CV, then which of the following is the most appropriate statistical decision and conclusion?
a. Reject H0, women don't feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
b. Reject H0, women feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
c. Reject H0, women definitely feel pressured at work to follow an implied dress code
d. Fail to Reject H0, women don't feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
e. Fail to Reject H0, women feel equally not at all, sometimes, and definitely pressured at work to follow an implied dress code
f. Fail to Reject H0, women definitely feel pressured at work to follow an implied dress code
10
40
70
7
Scenario 6: Use the following for problems 27 though 32. Is the successful completion of the extra credit problems related to the grade in the course? To answer this question, I took the data from our online Stat 2070 course this fall after the completion of the second test. For all 115 students I determined
Variable 1: How many extra credit points were earned through test 2 using the scale: 0, 1 to 5, 6 to 10, or 11+
Variable 2: Current grade in the course after test 2: A, B, C, or D/F
Here are the real data: Current Course Grade
A B C D/F
0
Extra 1 to 5
Credit 6 to 10
Points 11+
27. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
28. In the context of this scenario, which of the following is the most appropriate HA?
a. Extra credit points earned is related to current course grade
b. Students with 11+ extra credit points are more likely to have a current course grade of A
c. Students with 0 extra credit points are more likely to have a current course grade of D/F
d. b. and c.
29. Calculate the value of E for the (2,3) cell. (round off to 2 decimal places) __________
30. What is the value of the critical value? __________
31. In these data the cell (1,4) and the cell (4,1) have the 2 largest + (O-E) values. What is the appropriate conclusion based on the statistical decision to Fail to Reject H0?
a. Extra credit points earned is not related to current course grade
b. Students with 11+ extra credit points are more likely to have a current course grade of A
c. Students with 0 extra credit points are more likely to have a current course grade of D/F
d. b. and c.
32. In these data the cell (1,4) and the cell (4,1) have the 2 largest + (O-E) values. What is the appropriate conclusion based on the statistical decision to Reject H0?
a. Extra credit points earned is related to current course grade
b. Students with 11+ extra credit points are more likely to have a current course grade of A
c. Students with 0 extra credit points are more likely to have a current course grade of D/F
d. b. and c.
0
5
5
12
2
10
15
4
10
6
17
3
12
7
7
0
8
Scenario 7: Use the following for problems 33 though 39. Which of the 2 problems, the implementation of Obamacare or reducing the deficit, poses a greater risk to our economic future?" To answer this, I asked the following question to a sample of 900 economists, "Which of the following two issues poses the greater risk to our economic future: implementation of Obamacare (Obamacare) or reducing the deficit (Deficit)?" α= .05
[Let the outcome of interest be Obamacare]
Here are the results from this survey: Outcome f
Obamacare 513
Deficit 387
33. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
34. Given the information presented in the scenario, the appropriate null hypothesis is
a. Obamacare and Deficit are equally risky
b. Obamacare is related to Deficit
c. Obamacare is less of a risk than Deficit
d. Obamacare and Deficit are not equally risky
e. Obamacare is not related to Deficit
35. Given the information presented in the scenario, the appropriate alternative hypothesis is
a. Obamacare and Deficit are equally risky
b. Obamacare is related to Deficit
c. Obamacare is less of a risk than Deficit
d. Obamacare and Deficit are not equally risky
e. Obamacare is not related to Deficit
36. What is the numerical value of pˆ ? (round off to 2 decimal places) __________
37. What is the numerical value of p ? (round off to 2 decimal places) __________
38. If - CV < TS < CV , then
a. Reject H0 b. Fail to Reject H0 c. Not enough information provided to answer this question
39. If we Reject H0, then our conclusion for this scenario and these data would be
a. Obamacare and Deficit are equally risky
b. Obamacare is a greater risk than Deficit
c. Obamacare is less of a risk than Deficit
d. Obamacare and Deficit are not equally risky
Scenario 8: Use the following for problems 40 though 45. Do you feel more safe riding the subway in New York City or in Washington, D.C.? I asked a sample of riders of the NYC subway and another sample of riders of the DC subway the following question, "How safe do you feel riding the subway; 0 = Not Safe at All, 1 = It is scary, ...., 9 = Very Safe, 10 = So Safe that I never think about it?"
n Mean Variance
NYC Sample 10 4.0 2.8
DC Sample 10 5.5 2.0
40. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
41. What is the appropriate alternative hypothesis for this scenario?
a. Subway riders don't feel equally safe in New York City and in Washington D.C.
b. Subway riders feel safer in New York City than in Washington D.C.
c. Subway riders feel safer in Washington D.C. than in New York City
d. Subway riders feel equally safe in New York City and in Washington D.C.
42. What are the degrees of freedom for the appropriate test statistic? ________
43. Calculate the value of 2
p S . (round off to 2 decimal places) ________
44. If we Reject H0, then which of the following is the most appropriate conclusion?
a. Subway riders don't feel equally safe in New York City and in Washington D.C.
b. Subway riders feel safer in New York City than in Washington D.C.
c. Subway riders feel safer in Washington D.C. than in New York City
d. Subway riders feel equally safe in New York City and in Washington D.C.
45. If we Fail to Reject H0, then which of the following is the most appropriate conclusion?
a. Subway riders don't feel equally safe in New York City and in Washington D.C.
b. Subway riders feel safer in New York City than in Washington D.C.
c. Subway riders feel safer in Washington D.C. than in New York City
d. Subway riders feel equally safe in New York City and in Washington D.C.
Scenario 9: Use the following for problems 46 though 50. It has been hypothesized that the more frightened a person becomes the less information s/he seems to remember. In order to investigate this conjecture, I had a convenience sample of 30 people watch the horror movie "The Ring" and asked them "On a scale of 0 (not frightened at all) to 10 (Extremely frightened), how frightened were you?" I then gave them a memory test of 10 events shown in the movie. Each of the 30 people received a score (the number of events they recalled correctly) on the memory test from 0 to 10. Here are some results [Sp2 = 2.5, r = - .53] and
Standard
Mean Deviation
How frightened were you 8.5 2.4
Memory test 4.3 2.6
46. The appropriate test situation for this scenario is
a. One Sample Proportion
b. Multinomial
c. Homogeneity
d. Independent Samples t
e. Correlation
f. Independence
47. In the context of this scenario, which of the following is the most appropriate alternative hypothesis?
a. How frightened a person becomes is related to her/his score on the memory test
b. How frightened a person becomes is not related to her/his score on the memory test
c. The more frightened a person becomes the lower her/his score on the memory test
d. The more frightened a person becomes the higher her/his score on the memory test
e. The how frightened mean is higher than the memory test mean
48. What is the value of the critical value?
a. - 2.048 b. - 1.697 c. - 1.701 d. 2.048 e. 3.84
49. What is the value of the test statistic? (round off to 2 decimal places) __________
50. For this problem only, if the statistical decision was to Reject H0, then which of the following answers is the most appropriate conclusion?
a. How frightened a person becomes is related to her/his score on the memory test
b. How frightened a person becomes is positively related to her/his score on the memory test
c. How frightened a person becomes is negatively related to her/his score on the memory test
d. How frightened a person becomes is greater than her/his score on the memory test
e. None of the above