ECO2121 Basic Statistics: Problem Set 1

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ECO2121 Basic Statistics: Problem Set 1

Due Date: Feb 2 (Friday), 11:59pm

Total Points: 100

Instruction:  You can type or hand-write your answers. Please indicate clearly the question numbers. In the free response questions and data analysis questions, please show steps of calculation or detailed explanation. You are free to choose any software package in the data analysis questions. But be sure to present the machine outputs in human readable formats.

Academic Integrity: Copying is NOT allowed. If your answers are from collaborated work with other classmates, please cite properly. Identical answers in non-multiple-choice questions without citation are considered as cheating. For more details, please refer to the course syllabus.

Note: If possible, please scan your hand-written answers using APP like Adobe Scan in smart phones and upload your answers in .pdf format to the Blackboard. Please check the legibility of your file before uploading.

I. Multiple Choices (30 points in total, 3 point for each question)

1. Some hotels ask their guests to rate the hotel's services as excellent, very good, good, and poor. This is an example of the (choose the most precise one)

a.          ratio scale

b.          nominal scale

c.          interval scale

d.          ordinal scale

2. In a sample of 600 students in a university, 240, or 40%, are Economics majors. The 40% is an example of

a.          a sample

b.          a population

c.          descriptive statistics


d.          statistical inference

3. The average age in a sample of 900 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a.          must be more than 22, since the population is always larger than the sample 

b.          must be less than 22, since the sample is only a part of the population

c.          could not be 22

d.          could be larger, smaller, or equal to 22

Exhibit 1: Questions 4-6

The following is a frequency distribution table of the monthly expenditures for long distance telephone service of 200 households in Chattanooga.

Class

Expenditure ($)

# of households

1

0 and under 20

42

2

20 and under 40

64

3

40 and under 60

34

4

60 and under 80

28

5

80 and under 100

20

6

100 and over

12

4. Refer to Exhibit 1.  What is the cumulative relative frequency of the 2nd  class?

a.    .32

b.   .64

c.    .36

d.    .53

5. Refer to Exhibit 1.  What is the proportion of households with monthly expenditure for long distance service of either below $60 or at least $100?

a.    .70

b.   .76

c.    .84

d.    .53

6. Refer to Exhibit 1.  What percentage of households have monthly expenditure for long distance service between $40 and $100?

a.    54%

b.   82%

c.   27%

d.   41%

7. If the coefficient of variation is 40% and the mean is 70, then the standard deviation is

a.          28

b.          2800

c.          1.75

d.          784

8. Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win (earning 3 points), lose (earning 0 points) or tie (earning 1 points). The number  of possible scores for last 3 games is

a.           27

b.            3

c.            8

d.            9

9. Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is (assuming that a representative customer is indifferent between purchasing and not purchasing a computer)

a.         0.25

b.         0.50

c.          1.00

d.          0.75

10. Choose the summary measure that cannot be easily approximated from a boxplot.

a.          First Quartile

b.          Standard Deviation

c.          Median

d.          Inter Quartile Range

II. Free Response

Show detailed steps for the questions in this section.

1. (12 pts, 3 pts each) The highway patrol is interested in determining the average speed of automobiles traveling on I-75 between Chattanooga and Atlanta.  To accomplish this task, the speed of every tenth car passing a particular point on I-75 is recorded.


a.          What is the population for this study? Describe.

b.          What constitutes the sample?

c.          Is speed a categorical or a quantitative variable?

d.          What type of measurement scale is used?

2. (9 pts, 3 pts each) A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major

Graduate School

Business

Engineering

Others

Total

Yes

35

42

63

140

No

91

104

65

260

Total

126

146

128

400

a.    Are a majority of the seniors in the survey planning to attend graduate school?

b.    Compute row percentages and comment on the relationship between the students' undergraduate major and their intention of attending graduate school.

c.    Compute the column percentages and comment on the relationship between the students' intention of going to graduate school and their undergraduate major.

3. (12 pts, 3 pts each) A private research organization studying families in various countries  reported the following data for the amount of time 4-year-old children spent alone with their fathers each day.

Time with Dad

Country                                    (minutes)

Canada                                             44

China                                                54

Finland                                             50

Germany                                          36

Nigeria                                            42

Sweden                                             46

United States                                   42

For the above sample, determine the following measures:

a.    The mean

b.    The standard deviation

c.    The mode

d.    The 75th percentile

4. (12 pts, 3 pts each) The following is a frequency distribution for the ages of a sample of employees at a local company.

Age

Frequency

30 - 39

2

40 - 49

3

50 - 59

7

60 - 69

5

70 - 79

1

a.    Determine the average age for the sample.

b.    Compute the variance.

c.    Compute the standard deviation.

d.    Compute the coefficient of variation.


5. (9 pts, 3 pts each) Suppose a seller wants to find out the relationship of the price of his product  and its daily demand. He collects the following data of the daily demand (y in thousands of units) and the unit price (x in dollars) for some products.

Daily Demand (y)             Unit Price (x)

39                                     3

35                                     5

44                                     3

34                                     6

20                                     8

15                                   16

30                                     6

a.    Is the data set a sample or population?

b.    Compute and interpret the covariance between daily demand and unit price. 

c.    Compute and interpret the correlation coefficient.

6. (8 pts, 4 pts each) In a statistics class, the average grade on the final examination was 75 with a standard deviation of 5.  Use Chebyshev’s theorem to answer the following questions.

a.    At least what percentage of the students received grades between 50 and 100?

b.    Suggest an interval for the grades that will be true for at least 70% of the students. (Hint: Answer is not definite.)

7. (8 pts) The first seven (7) deviations from the mean for a random sample of 8 observations or cases (n=8) are

0.8,       2.1,       -2.5,      1.8,       0.2,       - 1.5,      1.8

What is the value for the 8th  deviation from the mean? SHOW WORK

2024-01-25