# ECO 578 Midterm Examination Questions and Answers

ECO 578 Midterm Examination Questions and Answers

Midterm  Exam

• There are 4 parts:

Part A: Answer the following questions (1-8)

Part B: True/ False (9-28)

Part C: Select the correct answer for the following questions (29-38)

Part D: Work Problem (39-50) **All work must be shown step by step**

• Two different ways to submit your answer sheet
1. Scan your answer sheet and place it in ONE FILE at drop-box.

(Make sure it is not zipped into one file.)

1. Use MS-Word and place it in a drop-box.

• **Excel is not acceptable for this test
• **Deadline: Monday, 22nd of February 2016 by noon
• **All work must be shown step by step in order to receive credit (Part D)

Part A: Answer the following questions (1-8)

1. Name 6 reasons why we use samples instead of an entire population.

1. Name 3 types of statistical samples

1. Name measures of spread or variability.

1. Name 4 types of random samples.

1. What are the uses of regression analysis?

1. Suppose the classes for an organized set of data are as follows: please fill in the A column and answer the B question.
 Class A. B. Mid-Point What is the value of class width? 0.235 – 0.875 0.875 – 1.515 1.515 – 2.155

1. Suppose the classes for an organized set of data are as follows and answer the A question:
 Class A.    Into which class is the value 14.6 assigned? 11.2 – 12.9 12.9 – 14.6 14.6 – 16.3

1. What is the standard deviation for these data: 5.784, 5.784, and 5.784

Part B: True or False (9-28)

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 29-33 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
• What is the frequency of the \$20,000-under \$30,000 class?
1. 20 b. 45 c. 70                d. 30

• What is the width of each class?
1. \$20,000 b. \$5,000 c. \$60,000       d. \$10,000

• What is the mid-point for the \$40,000-under \$50,000 class?
1. \$45,000 b. \$40,000 c. \$42,000       d. 15

• If we were to convert these data to a relative frequency distribution, what value would be associated with the \$50,000-under \$60,000 class?
1. 0.96 b. 0.06             c. 0.04             d. 0.12

• For a cumulative frequency distribution (less than or within), what value would be associated with the \$30,000-under \$40,000 class?
1. 30 b. 35                c. 165              d. 135

• For the value 10, 40, 20, 50, and 40, the value of the arithmetic mean is
1. 32 b. 40 c. 30                d. 34.5

• For the data values, 20, 31, 45, 54, 38, 33, 22, 45, and 17, the mode is
1. 33 b. 34 c. 38                d. 45

• The simplest measure of dispersion is the
1. Standard deviation. b. Variance.
2. Quartile deviation d. Range

• The largest value in a set of data is 240, and the lowest value is 100. If the resulting frequency distribution is to have seven classes of equal width, what will be the class width?
1. 12 b. 7 c. 5                  d. 20

• For the values 10, 20, 30, 40, and 50, the average absolute deviation from the mean is
1. 10 b. 15 c. 12                d. 14

Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (39-50)

1. Use the given information to answer the following questions:

 X 0 1 f 9 1

 a.       Range b.      Variance c.       Standard Deviation

1. Financial planners often recommend international mutual funds to boost the overall performance of an investor’s portfolio. The year’s performance figures for U.S. stock funds and for international stock funds are as follows, in percentages.

 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 (a-b).

 Year U.S. Stock Funds International Stock Funds X X2 X X2 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Total

1. Answer the following questions.

 Find:: U.S. Stock Funds International Stock Funds Mean Median

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

1. b) Using part (a), describe to an investor the differences between the distributions of the performance figures for the two types of stock funds.

1. This frequency distribution represents the commission earned (in dollar) by 100 salespeople employed at several branches of a large chain store. ( Using D-Method)
 Class Frequency CF Cumulative Relative Frequency Mid-point (X) d df d2 d2f 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)      3rd Quartile
1. Advertising expenditures constitute one of the important components of the cost of goods sold.  From the following data giving the advertising expenditures (in millions of dollars) of 50 companies, approximate the mean, median, and standard deviation of advertising expenditure.
 Advertising Expenditure Number of companies Cumulative Frequency Mid-point (X) d df d2 d2f 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.      50th Percentile c.       Mode d.      Range e.       Variance f.       Standard deviation g.      1rd Quartile
1. Work on problem 3 on page 3-49

1. Work on problem 4 on page 3-49(a-b)

 a) b)

1. Use problem 1on page 4-9 to answer the following questions(a-h);
 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
1. Fill in the blank and answer the following questions.
 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 P-value 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

1. Please use the given printout and answer the following questions.
 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 P-value 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

1. Work on problem 5 on page 5-12 (a-c)
 a) b) c)

1. Work on problem 11 on page 5-13 (a-c)
 a) b) c)

1. Work on problem 33 on page 5-18(a-e)
 a) b) c) d) e)