Economics 10A

Probability and Statistics in Economics I 




 

Answers to Quiz #1 for Econ 10a

 

1.         The nominal scale of measurement has the properties of the

            a.   ordinal scale

            b.   only interval scale

            c.   ratio scale

d.      None of the above answers is correct.

 

            Answer:  d

 

2.         Income is an example of a variable that uses the

            a.   ratio scale

            b.   interval scale

            c.   nominal scale

d.      ordinal scale

 

            Answer:  a

 

3.         Data

            a.   are always be numeric

            b.   are always nonnumeric

            c.   are the raw material of statistics

d.      None of the above answers is correct.

 

            Answer:  c

 

4.         The number of cases will always be the same as the number of

            a.   variables

            b.   elements

            c.   data sets

d.      data

 

            Answer:  b

 

5.         Social security numbers consist of numeric values.  Therefore, social security is an example of

            a.   a quantitative variable

            b.   either a quantitative or a qualitative variable

            c.   an exchange variable

d.      a qualitative variable

 

            Answer:  d

 

6.         The summaries of data, which may be tabular, graphical, or numerical, are referred to as

            a.   inferential statistics

            b.   descriptive statistics

            c.   statistical inference

d.      report generation

 

            Answer:  b

 

7.         The collection of all elements of interest in a particular study is

            a.   the population

            b.   the sampling

            c.   statistical inference

d.      descriptive statistics

 

            Answer:  a

 

8.         A statistics professor asked students in a class their ages.  On the basis of this information, the professor states that the average age of all the students in the university is 24 years.  This is an example of

            a.   a census

            b.   descriptive statistics

            c.   an experiment

d.      statistical inference

 

            Answer:  d

 

9.         If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the

            a.   fewest classes

            b.   most classes

c.       same number of classes as the other distributions since all are constructed from the same data

 

            Answer:  a

 

10.       The total number of data items with a value less than the upper limit for the class is given by the

            a.   frequency distribution

            b.   relative frequency distribution

            c.   cumulative frequency distribution

d.      cumulative relative frequency distribution

 

            Answer:  c

 

 

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. (Exhibit 2-2)

 

Undergraduate Major

 

Graduate School

Business

Engineering

Others

Total

Yes

70

84

126

280

No

182

208

130

520

Total

252

292

256

800

 

 

11.       Refer to Exhibit 2-2.  What percentage of the students' undergraduate major is engineering?

            a.   292

            b.   520

            c.   65

            d.   36.5

            Answer:  d

 

12.       Refer to Exhibit 2-2.  Of those students who are majoring in business, what percentage plans to go to graduate school?

            a.   27.78

            b.   8.75

            c.   70

d.      72.22

 

            Answer:  a

 

13.       The frequency distribution below was constructed from data collected on the quarts of soft drinks consumed per week by 20 students.

 

                        Quarts of Soft Drink                          Frequency

                                    0 -   3                                             4

                                    4 -   7                                             5

                                    8 - 11                                             6

                                   12 - 15                                            3

                                   16 - 19                                            2

 

            a.   Construct a relative frequency distribution.

            b.   Construct a cumulative frequency distribution.

            c.   Construct a cumulative relative frequency distribution.

            Answers:

 

 

a.

b.

c.

 

 

 

 

Cumulative

Quarts of

 

Relative

Cumulative

Relative

Soft Drinks

Frequency

Frequency

Frequency

Frequency

0 – 4

  4

0.20

4

0.20

4 - 8

  5

0.25

9

0.45

8 – 12

  6

0.30

15

0.75

12 – 16

  3

0.15

18

0.90

16 – 20

  2

0.10

20

1.00

Total

20

1.00

 

 

 

14.       The SAT scores of a sample of business school students and their genders are shown below.

SAT Scores

 

Gender

Less than 20

20 up to 25

25 and more

Total

Female

24

168

48

240

Male

40

96

24

160

Total

64

264

72

400

 

            a.   How many students scored less than 20?

            b.   How many students were female?

            c.   Of the male students, how many scored 25 or more?

            d.   Compute row percentages and comment on any relationship that may exist between SAT scores and gender of the individuals.

            e.   Compute column percentages.

 

            Answers:

            a.   64

            b.   240

            c.   24

            d.

SAT Scores

 

Gender

Less than 20

20 up to 25

25 and more

Total

Female

10%

70%

20%

100%

Male

25%

60%

15%

100%

 

            From the above percentages it can be noted that the largest percentages of both genders' SAT scores are in the 20 to 25 range.  However, 70% of females and only 60% of males have SAT scores in this range.  Also it can be noted that 10% of females' SAT scores are under 20, whereas, 25% of males' SAT scores fall in this category.

            e.

SAT Scores

 

Gender

Less than 20

20 up to 25

25 and more

Female

37.5%

63.6%

66.7%

Male

62.5%

36.4%

33.3%

Total

100%

100%

100%

 

15. For the following observations and its scatter diagram, please indicate what kind of relationship (if any) exist between x and y.

 

            x          y

            2          7

            6         19

            3          9

            5         17

            4         11

 

a positive relationship

 

16.       The sum of the relative frequencies for all classes will always equal

            a.   the sample size

            b.   the number of classes

            c.   one

d.      any value larger than one

 

            Answer:  c

 

 

17.       The mean of a sample

            a.   is always equal to the mean of the population

            b.   is always smaller than the mean of the population

            c.   is computed by summing the data values and dividing the sum by (n - 1)

d.      is computed by summing all the data values and dividing the sum by the number of items

 

            Answer:  d

 

18.       The median of a sample will always equal the

            a.   mode

            b.   mean

            c.   50th percentile

d.      all of the above answers are correct

 

            Answer:  c

 

A researcher has collected the following sample data (Exhibit 3-2)

 

            5          12        6            8         5

            6            7         5          12        4

 

19a.     Refer to Exhibit 3-2.  The median is

            a.   5

            b.   6

            c.   7

d.      8

 

            Answer:  b

 

19b.     Refer to Exhibit 3-2.  The mode is

            a.   5

            b.   6

            c.   7

d.      8

 

            Answer:  a

 

20.       The numerical value of the standard deviation can never be

            a.   larger than the variance

            b.   zero

            c.   negative

d.      smaller than the variance

 

            Answer:  c

 

21.       If two groups of numbers have the same mean, then

            a.   their standard deviations must also be equal

            b.   their medians must also be equal

            c.   their modes must also be equal

d.      None of these alternatives is correct

 

            Answer:  d

 

22.       Positive values of covariance indicate

            a.   a positive variance of the x values

            b.   a positive variance of the y values

            c.   the standard deviation is positive

d.      positive relation between the independent and the dependent variables

 

            Answer:  d

 

 

23.       Given the following information:

            Standard deviation = 8

            Coefficient of variation = 64%

            The mean would then be

            a.   12.5

            b.   8

            c.   0.64

d.      1.25

 

            Answer:  a

 

24.       A high school guidance counselor collected the following data about GPA and SAT math scores for six students:

 

            GPA  2.7  3.5  3.7  3.3  3.6  3.0

            SAT 450 560 700 620 640 570

 

Compute the sample correlation coefficient. What does this value tell us about the relationship between GPA and SAT?

 

            Answer:  0.871, positively linearly related.

 

25.       Consider the sample data in the following frequency table

 

Class

Midpoint

Frequency

3-7

5

12

8-12

10

5

13-17

15

2

18-22

20

1

 

 

            Compute the sample mean and sample standard deviation.

 

            Answer:  8,  4.41

 

 

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