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FAKULTAS EKONOMI DAN BISNIS - UNIVERSITAS INDONESIA

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FINAL TERM EXAM

SECOND SEMESTER OF ACADEMIC YEAR 2018/2019

ADVANCED STATISTICS / STATISTICS FOR ECONOMICS AND BUSINESS II

Date

:

Tuesday, May 28th, 2019

Time : 09.00-12.00

Lecturers : Team

Notes : You are allowed to use a calculator.

The use of mobile phones is not permitted and

mobile phones must be switched off during the

exams.

There are four problems for this exam. Each of problems equally contribute to your total grade.

Please answer all questions. Show your work!

Problem I: 25 POINTS

Stunting (or delayed child growth) has been a major health issue in Indonesia. The Government of Indonesia

(GoI) is planning to give a training to three selected groups: medical doctors, parents, and government

officials. The training materials are mostly focused on improving nutrition, enough exercise, and proper nap

time. However, the level of comprehension of each group is questionable. If each of the three groups have

the same initial knowledge about stunting, then similar training materials will be provided for each group.

Government statisticians are given a job to take samples of each group to test their prior knowledge about

stunting. If it is found that there is no difference in the scores of the prior knowledge across three groups, the

GoI will provide similar materials to each group. The scores and the ranks are provided in the following table.

Medical Doctors Parents Goverments

Score Rank Score Rank Score Rank

104 5.5 43 1 55 2

88 9 39 4 38 3

108 13 90 5.5 47 7

52 16 76 12 37 8

95 17.5 36 15 72 10

68 19 62 17.5 49 11

43 20 61 14

90 21

With the assumption of non-normal population and with the confidence level of 95%, please answer the

following questions.

a. State the null and alternative hypothesis. (2 points)

b. What sort of statistical method should we choose for testing the hypothesis? And why? (2 points)

c. What is the critical value for this test? (3 points)

d. What is the value of statistics from your calculation? (5 points)

e. Is there a significant evidence to reject H0? (5 points)

f. According to your answer, what should the GoI do with the training materials? (3 points)


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Problem II: 25 POINTS

A lecturer examines the relationship between the scores of Mathematics and Statistics tests. He uses a sample

consists of 14 students who took math and statistics tests. The following data represents student’s scores on

Math (X) and Statistic (Y).

Student Math score (X) Statistics score (Y)

1 97 89

2 68 57

3 85 87

4 74 76

5 92 97

6 92 79

7 100 91

8 63 50

9 85 85

10 87 84

11 81 91

12 93 91

13 77 75

14 82 77

(a) Draw a scatter plot between Math and Statistics scores. What could you say about the two variables

relation from the scatter plot? (5 points)

(b) Calculate and interpret the Spearman rank-order correlation coefficient (rho) between Math and

Statistics scores. (10 points)

(c) Specify competing hypotheses to determine whether the Spearman correlation coefficient differs from

zero. (2 points)

(d) At the 5% significant level, specify the critical value and decision rule. (5 points)

(e) Are Math and Statistics scores correlated? Explain. (3 points)

Problem III: 25 POINTS

A researcher intends to analyze the effect of per capita income (Million Rupiah/capita/year), price of rice

(Thousand Rupiah/kilogram), and regional status (City = 1 and Regency = 0) on average rice consumption

per capita in a week (kilogram/capita/week) in Central Java Province (consists of 6 cities and 29 regencies)

in 2019. The regression results are as follows. SUMMARY OUTPUT

Regression Statistics

Multiple R 0.9542

R Square 0.9106

Adjusted R Square …

Standard Error 0.0585

Observations 35

ANOVA

df SS MS F Significance F

Regression …. … … … 0.0000

Residual … 0.1060 … Total … 1.1860


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Coefficients Standard Error t Stat P-value

Intercept 0.1534 0.1057 … 0.1567

Income per Capita 0.1399 0.0091 … 0.0000

Price -0.0066 0.0075 … 0.3831

Regional Status -0.2424 0.0397 … 0.0000

a. Find the missing values in the tables. (5 points)

b. Formulate the estimated regression equation. (3 points)

c. Using ANOVA, find the global test and interpret the result (3 points)

d. Using α = 5%, are those independent variables significant? (5 points)

e. Interpret:

i. The Income per Capita coefficient. (3 points)

ii. The Regional Status coefficient. (3 points)

f. What is the average rice consumption per capita in a week in Kebumen Regency if the income per capita

is Rp. 8 million/capita/year and the price of rice is Rp. 9 thousand/ kilogram? (3 points).

Problem IV: 25 POINTS

You are given the following quarterly sales information for SMART Company over the last 3 years.

Tahun Quarter Sales

Four-period

moving

average

CMA Ratio to

CMA

Seasonal

Index

Deseasonalized

(Rp Billion) Sales

2016 1 38

2016 2 37

38.5

2016 3 39

38.9

2016 4 40

39.1

2017 1 39.4

39.4

2017 2 38

39.8

2017 3 40.2

40.2

2017 4 41.4

40.9

2018 1 41

41.6

2018 2 40.8

42.3

2018 3 43

2018 4 44.4

a. Graph the sales data. (4 points)

b. Find the centered moving averages (CMA). (3 points)

c. Use your results from part b to construct the seasonal and irregular components of the data. (3 points)

d. Use your results from part c to separate the seasonal and irregular components of the time series and

obtain the seasonal index for each quarter. (4 points)


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e. Use your results from part d to seasonally adjust the original sales data. Has the adjustment removed

the seasonal effect? (6 points)

f. The results of a linear trend regression on the deseasonalized sales data computed in part e to forecast

sales value is given in the table below. What is the sales revenue in million rupiah for the third and

fourth quarters in 2019? (5 points)

ANOVA

df SS MS F Significance

F

Regression 1 32.42641 32.42641 172.3235 0.0000 Residual 10 1.881718 0.188172 Total 11 34.30813

Coefficients

Standard

Error t Stat p-value Lower 95% Upper 95%

Intercept 37.1034 0.2670 138.9754 0.0000 36.5085 37.6982

T 0.4762 0.0363 13.1272 0.0000 0.3954 0.5570


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Appendix-1: Selected Formulas

( )( )( )1 X Y

X X Y Yr

n S S

− −=

−

𝒓𝑺 = 𝟏 −

𝟔 ∑ 𝒅𝒊𝟐

𝒏(𝒏𝟐−𝟏)

2

2

1s

S

nt r

r

−=

−

𝑯 = (𝟏𝟐

𝒏(𝒏+𝟏)∑

𝑹𝒊𝟐

𝒏𝒊

𝒌𝒊=𝟏 ) − 𝟑(𝒏 + 𝟏) 𝑹𝟐 = 𝟏 −

𝑺𝑺𝑬

𝑺𝑺𝑻

2 11 ; k = number of dependent variables

1

adj

SSE

n kRSST

n

− −= −

−

𝑭(𝒅𝒇𝟏,𝒅𝒇𝟐) = 𝑺𝑺𝑹/𝒌

𝑺𝑺𝑬/(𝒏−𝒌−𝟏)=

𝑴𝑺𝑹

𝑴𝑺𝑬

𝒕𝒅𝒇 = 𝒃𝒋 − 𝜷𝒋𝟎

𝑺𝒃𝒋

𝑹𝒂𝒕𝒊𝒐 − 𝒕𝒐 − 𝒎𝒐𝒗𝒊𝒏𝒈 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 = 𝒚𝒕

𝒚�̅�

𝑼𝒏𝒂𝒅𝒋𝒖𝒔𝒕𝒆𝒅 𝑺𝒆𝒂𝒔𝒐𝒏𝒂𝒍 𝑰𝒏𝒅𝒆𝒙 = 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒐𝒇 𝒚𝒕

𝒚�̅� 𝒇𝒐𝒓 𝒆𝒂𝒄𝒉 𝒔𝒆𝒂𝒔𝒐𝒏

𝑨𝒅𝒋𝒖𝒔𝒕𝒆𝒅 𝑺𝒆𝒂𝒔𝒐𝒏𝒂𝒍 𝑰𝒏𝒅𝒆𝒙 = 𝑼𝒏𝒂𝒅𝒋𝒖𝒔𝒕𝒆𝒅 𝑺𝒆𝒂𝒔𝒐𝒏𝒂𝒍 𝑰𝒏𝒅𝒆𝒙 × 𝒄𝒐𝒓𝒓𝒆𝒄𝒕𝒊𝒐𝒏 𝒇𝒂𝒄𝒕𝒐𝒓

𝑺𝒆𝒂𝒔𝒐𝒏𝒂𝒍𝒍𝒚 𝑨𝒅𝒋𝒖𝒔𝒕𝒆𝒅 𝑺𝒆𝒓𝒊𝒆𝒔 = 𝒚

�̂�


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Appendix 2: Standard Normal Curve Areas


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Appendix-3: Student’s t Distribution


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Appendix-4: F Distribution


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Appendix-4: F Distribution (Continued)


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Appendix-5: Chi-Square Distribution

Documents

FINAL TERM EXAM SECOND SEMESTER OF ACADEMIC YEAR …kanopi-febui.org/wp-content/uploads/2020/03/Soal... · 104 5.5 43 1 55 2 88 9 39 4 38 3 108 13 90 5.5 47 7 52 16 76 12 37 8 95