ECO 578 Midterm Examination Questions and Answers
Midterm Exam
Part A: Answer the following questions (18)
Part B: True/ False (928)
Part C: Select the correct answer for the following questions (2938)
Part D: Work Problem (3950) **All work must be shown step by step**
(Make sure it is not zipped into one file.)
Part A: Answer the following questions (18)
Class  A.  B. 
MidPoint  What is the value of class width?  
0.235 – 0.875  
0.875 – 1.515  
1.515 – 2.155 
Class  A. Into which class is the value 14.6 assigned? 
11.2 – 12.9  
12.9 – 14.6  
14.6 – 16.3 
Part B: True or False (928)
Please put T or F in the column T or F box
T  F  
9  For the data, 35, 22, 18, and 25, the value of the median is 20.  
10  The random sample is the most important, because statistical theory applies to it alone  
11  Sturges’ rule is used to determine whether a frequency distribution can be constructed for a given set of data.  
12  The sum of the class frequencies is equal to the number of observations made  
13  A relative frequency distribution describes the proportion of data values that fall within each category  
14  There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations.  
15  Planning is the most important step in a statistical study  
16  The following number of student enrolled in 10 elective English classes offered during the year at a community college: 11, 24, 15, 14, 15, 13, 26, 15, 10, 14 The modal class size was 14  
17  Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations  
18 
The following data, reported by a sample of students, are the number of movies seen in a movie theatre during past six months. 6 6 9 12 6 4 8 15 6 The frequency of students who saw 6 movies is 6. 

19  The arithmetic mean is the sum of the data values divided by the number of observations.  
20  is  
21  means that A and B are mutually exclusive events.  
22 
Mutually exclusive events imply that if one event occurs, the other cannot occur. An event (e.g.,) and its complement are always mutually exclusive. 

23  
24  When events are not mutually exclusive, the rule is:  
25  Rule of addition when event are mutually exclusives:  
26  is not  
27  The P(x) is always 0 ≤ P(x) ≤ 1.  
28  Events are independent when the occurrence of one event has no effect on the probability that another will occur. 
Part C: Multiple Choice (29–38)
Questions 2933 refer to the following frequency distribution:
Annual Income  Number of households 
under $10,000  20 
$10,000 – under $20,000  45 
$20,000 – under $30,000  70 
$30,000 – under $40,000  30 
$40,000 – under $50,000  15 
$50,000 – under $60,000  12 
$60,000 – under $70,000  8 
Total  200 
Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (3950)
X  0  1 
f  9  1 
a. Range 

b. Variance 

c. Standard Deviation 

Year  U.S. Stock Funds  International Stock Funds 
1983  21.77  27.73 
1984  1.20  4.71 
1985  28.52  44.44 
1986  14.53  41.40 
1987  1.17  7.02 
1988  15.75  17.43 
1989  25.09  21.98 
1990  6.11  12.07 
1991  36.67  12.51 
1992  9.11  4.48 
1993  9.17  25.65 
(Adapted from ‘International Aid,’ USA Today, October4, 1993, p.3B.)
Use the given information and fill in the table and answer the following question (ab).
Year  U.S. Stock Funds  International Stock Funds  
X  X^{2}  X  X^{2}  
1983  
1984  
1985  
1986  
1987  
1988  
1989  
1990  
1991  
1992  
1993  
Total  
Find::  U.S. Stock Funds  International Stock Funds 
Mean 


Median 

Find::  U.S. Stock Funds  International Stock Funds 
Range 


Variance 


S.D. 

Class  Frequency  CF  Cumulative Relative Frequency  Midpoint (X)  d  df  d^{2}  d^{2}f 
150 – 158  0.05  3  
159 – 167  0.21  2  
168 – 176  0.41  1  
177 – 185  0.62  0  
186 – 194  0.82  1  
195 – 203  0.97  2  
204 – 212  1.00  3  
Total  1.00 
a) Mean

b) Median 
c) Mode

d) Range 
e) Variance

f) Standard deviation 
g) 3^{rd} Quartile

Advertising Expenditure  Number of companies  Cumulative Frequency  Midpoint (X)  d  df  d^{2}  d^{2}f 
25 and under 35  5  2  
35 and under 45  18  1  
45 and under 55  11  0  
55 and under 65  6  1  
65 and under 75  10  2  
Total  50 
b) Mean

b. 50^{th} Percentile 
c. Mode

d. Range 
e. Variance

f. Standard deviation 
g. 1^{rd} Quartile

a)

b) 
a) Find

b) Find 
c) Interpret the meaning of

d) Find the regression equation

e) Predict the case sales for a brand with a media expenditure of $80

f) Compute the coefficient of determination 
g) Interpret the coefficient of determination

h) Compute and interpret the coefficient of correlation

SUMMARY OUTPUT  
Regression Statistics  
Multiple R  ______  
R Square  ______  
Adjusted R Square  0.8906  
Standard Error  13.8293  
Observations  ______  
ANOVA  
df  SS  MS  F  Significance F  
Regression  1  14200  14200  ______  ______  
Residual  8  ______  191.25  
Total  9  15730  
Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0%  
Intercept  60  9.2260  6.5033  0.0002  ______  81.2753  38.7247  ______ 
X  5  0.5803  ______  0.0003  ______  6.3381  3.6619  ______ 
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

SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.9630  
R Square  0.9274  
Adjusted R Square  0.9129  
Standard Error  1.5510  
Observations  7  
ANOVA  
df  SS  MS  F  Significance F  
Regression  1  153.7199  153.7199  63.8974  0.0005  
Residual  5  12.0287  2.4057  
Total  6  165.7486  
Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0%  
Intercept  17.9276  10.1053  1.7741  0.1362  43.9042  8.0490  43.9042  8.0490 
Income Rate ($1000)  1.0946  0.1369  7.9936  0.0005  0.7426  1.4466  0.7426  1.4466 
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

a)

b) 
c)

a)

b) 
c)

a)

b) 
c)

d) 
e)
