# ECO 578 midterm exam FALL 2015

Question

vPart A: Multiple Choice (1–16)

Using the following information to answer questions 1-8:

2

1

3

0

1

2

0

5

1

4

_____1. What is the mean?

a) 1.90

b) 2.11

c) 1.73

d) 1.66

_____2. What is the median?

a) 1.00

b) 1.50

c) 1.60

d) 1.90

_____3. What is the mode?

a) 0

b) 1

c) 2

d) 3

_____4. What is the range?

a) 1

b) 4

c) 5

d) 3

_____5. What is the variance?

a) 1.66

b) 2.77

c) 1.76

d) 3.11

_____6. What is the standard deviation?

a) 1.66

b) 2.77

c) 1.76

d) 3.11

_____7. What is the 1st quartile?

a) 0

b) 1

c) 2

d) 3

_____8. What is the 70th percentile?

a) 1

b) 1.5

c) 2

d) 2.5

Questions 9-16 refer to the following frequency distribution:

The following information represents the number of tons of grain stored at the 60 grain elevators of central Soya, Inc.

Class

Frequency

_____9. What is the relative frequency for the class 170-174?

a) 16

b) 36

c) 0.27

d) 0.60

_____10. What is the mean?

a) 170.25

b) 12

c) 172.75

d) 167

_____11. What is the median?

a) 169.5

b) 170

c) 172.63

d) 173.13

160-164

6

165-169

14

170-174

16

175-179

13

180-184

11

Total

60

_____12. What is the mode?

a) 16

b) 170

c) 172

d) 174

_____13. What is the variance?

a) 39.68

b) 12.33

c) 151.55

d) 149.02

_____14. What is the standard deviation?

a) 6.30

b) 3.51

c) 12.31

d) 12.21

_____15. What is the 1st quartile?

a) 168.21

b) 167.07

c) 167.57

d) 167.71

_____16. What is the 70th percentile?

a) 176.35

b) 176.85

c) 176.81

d) 177.31

vPart B: True or False (17-30)

_____17. The random sample is the most important, because statistical theory applies to it alone.

_____18. In a frequency distribution, the class mark is the number of observations that fall within that class.

_____19. Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations.

_____20. The sum of the class frequencies is equal to the number of observations made.

_____21. A relative frequency distribution describes the proportion of data values that fall within each category.

_____22. There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations.

_____23. The arithmetic mean is the sum of the data values divided by the number of observations.

_____24. is

_____25. The median always exists in a set of numerical data.

_____26. means that A and B are mutually exclusive events.

_____27. Mutually exclusive events imply that if one event occurs, the other cannot occur. An event (e.g.,) and its complement are always mutually exclusive.

_____28.

_____29. Events are independent when the occurrence of one event has no effect on the probability that another will occur.

_____30. The P(x) is always 0 ≤ P(x) ≤ 1.

vPart C: Answer the following questions (31-39)

31. Name 3 types of statistical samples

1

2

3

32. Name reasons why we use samples instead of an entire population

33. Name types of random samples.

34. Name the measure of central tendency.

35. Name measures of spread or variability.

36. Show that you understand the difference between a sampling error and a sampling bias.

37. Name 4 parts of the regression.

38. When do we use the regression?

39. Explain the concept of error and uncertainty as it relates to decision making.

vPart D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (40-50)

40. Train A and Train B are two transportations that people can use to transport from Boston to New York. Sample of times recorded in minutes for each train are shown below.

Train A

28

29

32

37

33

25

29

32

41

34

Train B

29

31

33

32

34

30

31

32

35

33

Please answer the following questions (a-i).

Train A

Train B

a) Mean

b) Mean

c) Median

d) Median

e) Variance

f) Variance

g) Standard deviation

h) Standard deviation

i) From above computed results from Train A and Train B, what train should be preferred and why?

41. Use the information from the problem number 5 on page 3-21 to fill in the given table below and answer the following questions (a-h) (**Using D-method).

Number of miles flown

Number of frequent

Flyers (f)

CF

MidPoint

(x)

d

fd

d2

fd2

(1,000)

-1

0

1

2

3

4

Total

a) Find mean

b) Find median

c) Find mode

d) Find Range

e) Find variance

f) Find standard deviation

g) Find 1st Quartile

h) Find 99th percentile

42. Use the information from the problem number 1 on page 3-39 to fill in the given table below and answer the following questions (a-h) (**Using D-method).

Dinner Check

Frequency

(f)

CF

MidPoint

(x)

d

fd

d2

fd2

($)

-2

-1

0

1

2

3

Total

a) Find mean

b) Find median

c) Find mode

d) Find Range

e) Find variance

f) Find standard deviation

g) Find 3rd Quartile

h) Find 80th percentile

43. The mean GMAT score of 65 applicants who were accepted into the MBA program of Xavier Business School was 520 with variance of 225. About how many applicants scored between 470 and 570 on the GMAT?

44. Work on problem number 11 on page 3-49 (a-b).

a)

b)

45. Use the information from the problem number 2 on page 4-8 and answer the following questions (a-h); Given that Y = Income rate and X = Average expense

a) Find

b) Find

c) Interpret the meaning of

d) Find the regression equation

e) Predict the income rate for an area with an average expense of $75

f) Compute the coefficient of determination

g) Interpret the coefficient of determination

h) Compute and interpret the coefficient of correlation

46. An educator wants to see how strong the relationship is between a student’s score on a test and his or her grade-point average. The data obtained from the sample are shown.

Test Score (X)

98

105

100

100

106

95

116

112

GPA (Y)

2.1

2.4

3.2

2.7

2.2

2.3

3.8

3.4

a) Find

b) Find

c) Interpret the meaning of

d) Find the regression equation

e) Predict the GPA for a student who gets 145 in the test score.

f) Compute the coefficient of determination

g) Interpret the coefficient of determination

h) Compute and interpret the coefficient of correlation

47. Please use the given printout and answer the following questions.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.190885429

R Square

0.036437247

Adjusted R Square

-0.44534413

Standard Error

2.502630195

Observations

4

ANOVA

df

SS

MS

F

Significance F

Regression

1

0.473684211

0.47368421

0.0756303

0.809114571

Residual

2

12.52631579

6.26315789

Total

3

13

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

2.894736842

1.904216054

1.52017248

0.2678372

-5.298443561

11.08792

X Variable

-0.315789474

1.148285486

-0.2750095

0.8091146

-5.256463153

4.624884

a) What is

b) What is

c) Interpret the meaning of

d) What is the regression equation

e) What is the coefficient of determination

f) What is the coefficient of correlation

g) Interpret the coefficient of determination

h) Interpret the coefficient of correlation

48. From the below cross classification showing the frequencies of hair and eye color of a group of students at North Texas, and answer the following questions (a-d).

Eye Color

Hair Color Blond

Brown

Blue

Green

Hazel

Total

Blond

30

18

7

2

57

Brown

74

28

10

7

119

Red/Auburn

17

15

5

3

40

Black

43

11

6

1

61

Total

164

72

28

13

277

a) Probability that a student will have blue eyes given he/she is blond.

b) Probability of black hair.

c) Probability that a student will have either red hair or green eyes.

d) Probability that a student will have brown hair and brown eyes.

49. Work on problem number 33 on page 5-19 (a-d)

a)

b)

c)

d)

50. Work on problem number 17 on page 5-16 (a-e)

a)

b)

c)

d)

e)

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