ECO 578 Summer I 2016

ECO 578 Summer I 2016

Part A: Answer the following questions (1-10)

What are the measures of central tendency?

What are the characteristics of mean, median, and mode?

What is the sampling error?

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

Name measures of spread or variability.

Explain the concept of error and uncertainty as it relates to decision making.

As discussed in the class live, what are 3 ways of calculating R2?

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

Into which class is the value 14.6 assigned? (Circle your answer)

Class

a.

11.2 – 12.9

b.

12.9 – 14.6

c.

14.6 – 16.3

What is the standard deviation for these data: 3.784, 3.784, and 3.784

Part B: True or False (11-30)

______11. The random sample is the most important, because statistical theory applies to it alone.

______12. In a frequency distribution, the class mark is the number of observations that fall within that class.

______13. Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations.

______14. The sum of the class frequencies is equal to the number of observations made.

______15. Planning is the most important step in statistical studies.

______16. Systematic, stratified and cluster sampling are not approximations to simple random sampling.

______17. A relative frequency distribution describes the proportion of data values that fall within each category.

______18. There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations.

______19. is

______20. The median always exists in a set of numerical data.

______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. Events are independent when the occurrence of one event has no effect on the probability that another will occur.

______28.The P(x) is always 0 ≤ P(x) ≤ 1.

______29. The mean of the discrete probability distribution for a discrete random variable is called its expected value.

______30. A random variable is a variable that can take different values according to the outcome of an experiment, and it can be either discrete or continuous.

Part C: Multiple Choice (31–40)

Use the following data to answer question 31-36 :

20

31

45

54

38

33

22

45

17

_____ 31. The Mode is______

33 b. 34 c. 38 d. 45

_____ 32. The 50th percentileis______

33 b. 35 c. 45.5 d. 45

_____ 33. The Mean is______

33.89 b. 34.89 c. 38.13 d. 32.13

_____ 34. The Variance is______

139.43 b. 162.11 c. 154.27 d. 149.07

_____ 35. The Standard deviation is______

11.81 b. 12.73 c. 12.42 d. 12.21

_____ 36. The Range is______

25 b. 28 c. 34 d. 37

Select the best answer for question 37-40 :

_____ 37. The simplest measure of dispersion is the

a. Standard deviation. b. Variance.

c. Quartile deviation d. Range

_____ 38. 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

_____ 39. 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

_____ 40. A simple random sample for five executives who went on a diet on their doctor’s order report the following numbers of pounds lost during their first two weeks on the diet: 5,8,3,7,8. What is the variance for this sample?

a. 4.7 b. 3.76 c. 1.94 d. 2.17

Part D:Must show all your work step by step in order to receive full credit; Excel is not allowed. (41-55)

Use the given information to answer the following questions:

X

0

1

f

9

1

Range

Variance

Standard deviation

Use the given information to answer the following question

Y

X

3

1

9

5

a) Compute the value of

Compute the value of

Interpret the meaning of

Find the regression equation.

The length of stay in a hospital for major surgery is recorded for a sample of 48 patients: (a-h)

Length of Stay (Days)

12

13

14

15

Patient Count

22

2

8

16

a) Mean

Median

Mode

Range

Variance

Standard deviation

95th Percentile

3nd Quartile

Use the problem number 3 on page 3-19 to fill and complete table, then answers the following questions (a-h). (**Using D-Method)

Score

Frequency

Mid-point (X)

Cf

d

df

f

-2

-1

0

1

2

Total

a) Mean

Median

Mode

Range

Variance

Standard deviation

45th Percentile

1st Quartile

Please fill and complete the following table, then answer the following questions (a-h). (**Using D-Method)

Age (in years)

Frequency

Mid-point (X)

Cf

fx

d

df

d2

fd2

20 – 24

10

-3

25 – 29

19

-2

30 – 34

27

-1

35 – 39

16

0

40 – 44

10

1

45 – 49

6

2

50 – 54

5

3

55 – 59

3

4

Total

a) Mean

Median

Mode

Range

Variance

Standard deviation

45th Percentile

1st Quartile

Use problem 11 on page 4-11 to answer the following questions (a-e):

Find

Find

Interpret the meaning of

Find the regression equation

Predict the average value of Y for X=6

Work on problem 33 on page 5-19 (a-d):

a)

b)

c)

d)

Use the information from problem 15 on page 4-12 to fill in the given table, then answer the following questions (a-g). Giving that Y=Income, X=Expense

Area

Y ($1000)

X ($1000)

XY

X2

Y2

Income Rate

Average Expense

Total

a) Compute the value of

Compute the value of

Interpret the meaning of

Find the regression equation.

Compute the Coefficient of determination.

Predict the income rate for an area with an average expense of $75

Interpret the Coefficient of determination

Please fill in the blank and answer the following questions:

SUMMARY OUTPUT

Regression Statistics

Multiple R

__________

R Square

__________

Adjusted R Square

0.125

Standard Error

__________

Observations

__________

ANOVA

df

SS

MS

F

Significance F

Regression

1

0.828

__________

__________

0.2308

Residual

__________

2.227

__________

Total

6

__________

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

112.413

9.484

11.853

7.52722E-05

88.033

136.793

__________

__________

X

-19.137

14.033

-1.364

0.231

-55.211

16.937

__________

__________

What is

What is

Interpret the meaning of

What is the regression equation

What is the coefficient of determination

What is the coefficient of correlation

Interpret the coefficient of determination

Interpret the coefficient of correlation

Work on problem 5 on page 5-13

a)

b)

c)

Work on problem 16 on page 5-15 only part b (1-7).

1)

2)

3)

4)

5)

6)

7)

Work problem number 5 on page 6-13 (a-e).

a)

b)

c)

d)

e)

Work on problem 13 on page 6-15

a)

b)

c)

d)

e)

Use problem number 4 on page 6-22 to fill in the table and answer the following questions (a-c).

X

P[X=x]

(X)(P[X=x])

[X-E(X)]

[X-E(X)]2

[X-E(X)]2 P[X=x]

0

1

2

3

4

5

6

Total

a) Expected value

b) Variance

c) Standard deviation

Work on problem 8 on page 6-14 (a-b):

a)

b)