ECO 578 FINAL EXAM (SPRING 2016)

Name: _________________

                                                                                                               ID:  _________________

                                    Online Exam I

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

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

2.     Name 3 types of statistical samples

3.     Name measures of spread or variability.

4.     Name 4 types of random samples.

5.     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

8.     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

______29.       What is the frequency of the $20,000-under $30,000 class?

a. 20               b. 45                c. 70                d. 30

______30.       What is the width of each class?

a. $20,000      b. $5,000         c. $60,000       d. $10,000

______31.       What is the mid-point for the $40,000-under $50,000 class?

a. $45,000      b. $40,000       c. $42,000       d. 15

______32.       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?

            a. 0.96             b. 0.06             c. 0.04             d. 0.12

______33.       For a cumulative frequency distribution (less than or within), what value would be associated with the $30,000-under $40,000 class?

            a. 30                b. 35                c. 165              d. 135

______34.       For the value 10, 40, 20, 50, and 40, the value of the arithmetic mean is

a. 32               b. 40                c. 30                d. 34.5

______35.       For the data values, 20, 31, 45, 54, 38, 33, 22, 45, and 17, the mode is

a. 33               b. 34                c. 38                d. 45

______36.       The simplest measure of dispersion is the

a. Standard deviation.                       b. Variance.   

c. Quartile deviation             d. Range

______37.       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?

a. 12               b. 7                  c. 5                  d. 20

______38.       For the values 10, 20, 30, 40, and 50, the average absolute deviation from the mean is

a. 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

40.  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

a)     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.

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

&