ECON10005 Chapter Notes - Chapter 3: Central Limit Theorem, Variance, Bias Of An Estimator

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sapphireporpoise122

25 Aug 2018

School

University of Melbourne

Department

Economics

Course

ECON10005

Professor

All

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Document Summary

Statistical inference is a collection of procedures designed so that data in a sample can be informative in a rigorous way about a particular population. A sample is randomly drawn from a population in a manner designed to provide a representative sample. (i. e. a sample that provides "reliable inference" about the population) Sample: x, (cid:1871)2 (estimators of population parameter) Every individual in the population has an equal probability of being in the sample. Every individual is chosen (or not chosen) independently of every other individual. Suppose 1, 2, (cid:1866) take only values 0 or 1 ( = 1) = (cid:1868) The number of 1"s in the sample is (cid:1866) 1. The sample proportion or sample mean is: Variance of the sample mean (n: sample size) population mean. Different samples -> different x (i. e: x is a random variable) Increasing n -> better x because it evaluates more precisely relative to the.

Related Questions

. Suppose Y is related to R and S in the following nonlinear way:

Y= aRáµSá¶

a. How can this nonlinear equation be transformed into a linear form that can ve analyzed using multiple regression analysis.

Sixty-three observations are used to obtain the following regression results:

DEPENDENT VARIABLE: LNY		R-SQUARE	F-RATIO	P-VALUE ON F
OBSERVATION: 63		0.8151	132.22	0.0001
VARIABLE	PARAMETER ESTIMATE	STANDARD ERROR	T-RATIO	P-VALUE
INTERCEPT	-1.386	0.83	-1.67	0.1002
LNR	0.452	0.175	2.58	0.0123
LNS	0.30	0.098	3.06	0.0033

b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?

c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value of the F-statistic.

d. How well does this nonlinear model fit the data?

e. Using the estimated value of the intercept, compute an estimate of a.

f. If R = 200 and S = 1,500, compute the expected value of Y.

g. What is the estimated elasticity of R? Of S?

silvercheetah101

1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?

A. Alpha and Delta

B. Delta and Gamma

C. Alpha and Gamma

D. Standard Deviation and Mean

3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.

A. Ho: r = .05 p < .5

B. Ho: r = 0 p >.05

C. Ho: r ? 0 p?.05

D. Ho: r = 0 p?.05

In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable?

A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.

5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied?

A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12^th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12^th lag.

C. No. Only the 12 lag period is not correlated.

D. You cannot tell since the number of sample observations is not provided.

E. The p-value is above .05 so the data is correlated.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3^rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

1. Which of the following is an example of the source function of the environment?

A. Trees absorb some of the carbon dioxide emitted by human activity

B. Wetlands reduce the pollution levels in water

C. Winds carry air pollution away from a city

D. Humans harvest fish from the oceans

E. Bacteria break down discarded wastes

2. What is the primary external input into the broader ecological circular flow model?

A. Pollution

B. Solar energy

C. Fossil fuels

D. Geophysical cycles

E. Factors of production

3. What is the key reason that Malthusian predictions have not come true so far?

A. Increasing productivity per capita

B. Increasing population

C. Increasing natural capital

D. Increasing population density

E. Definition of property rights

4. Which one of the following statements is true regarding the rate of global population growth over the last 40 years?

A. Population has grown at a faster rate than agricultural production and energy use

B. Population has grown faster than energy use but not agricultural production

C. Population has grown faster than agricultural production but not energy use

D. Population, energy use, and agricultural production have all grown at about the same rate

E. Population has grown at a slower rate than agricultural production and energy use

5. Which one of the following is not a possible way to internalize externalities?

A. Eliminate government intervention

B. Raise taxes

C. Create subsidies

D. Create a system of tradable permits

E. Create new regulations

6. The efficient price of a license fee is determined by the difference between ...

A. Marginal revenue and marginal cost

B. Average revenue and marginal cost

C. Total revenue and total cost

D. Average revenue and total cost

E. Total revenue and marginal cost

7. Valuing environmental services based on estimating the value of different characteristics of market goods is called ...

A. Travel cost method

B. Contingent valuation

C. Hedonic pricing

D. Production function valuation

E. Avoided cost valuation

8. Which one of the following statements about national accounting is false?

A. Gross National Product does not account for natural capital depreciation

B. Net investment is gross investment minus depreciation

C. Capital depreciation accounts for wearing-out of human-made capital over time

D. A negative net investment implies a decline in national wealth

E. Net National Product does not account for capital depreciation

9. User costs will be incorporated into a market if ...

A. Interest rates are positive

B. Discount rates are zero

C. Resource owners foresee future shortages

D. Government intervention is eliminated

E. Discount rates are positive

10. Hotellingâs rule states that...

A. The net price of a resource is constant

B. The net price of a resource rises at a rate equal to the interest rate

C. The net price of a resource declines at a rate equal to the interest rate

D. The price of a resource depends on the allocation of property rights

E. The price of a resource is efficient as long as all user costs are internalized

11. Transferable permits are likely to result in less inefficiency, relative to a pollution tax, when...

A. The marginal costs of damage are steep and the marginal costs of pollution reduction are relatively stable

B. The marginal costs of damage are steep and the marginal costs of pollution reduction are steep

C. The marginal costs of damage are relatively stable and the marginal costs of pollution reduction are relatively stable

D. The marginal costs of damage are relatively stable and the marginal costs of pollution reduction are steep

E. The marginal costs of damage are elastic and the marginal costs of pollution reduction are also elastic

12. Which one of the following statements is false regarding a transferable pollution permit system?

A. Each firm will operate in an economically efficient manner

B. Total pollution levels in a region can be set by the government

C. The price of a permit will vary with changes in technology

D. The system is preferable to a pollution tax in all situations

E. Social benefits can be maximized

13. If a large percentage of people in a country are young, this is a sign that ...

A. The country has significant population momentum

B. The country is in the first stage of the demographic transition

C. The countryâs population will shortly stabilize

D. The countryâs population is declining

E. The country is in the last stage of the demographic transition

14. Which one of the following statements about the demographic transition theory is false?

A. Population levels are relatively stable in the first and last stages of the demographic transition

B. The demographic transition theory states that death rates will decrease before birth rates decrease

C. Many industrial countries have entered the third or fourth stage of the demographic transition

D. The demographic transition process has occurred at very different rates in different parts of the world

E. The demographic transition theory suggests that continued exponential population growth is possible with constant economic growth

15. Which one of the following policies would not reduce water use?

A. Full marginal-cost pricing

B. Microirrigation technology

C. Reusing wastewater for industrial uses

D. Subsidizing irrigation systems

E. Removing water subsidies

16. Which one of the following statements is false?

A. Carbon dioxide is a stock pollutant

B. Without the natural greenhouse effect, life could exist on earth

C. The atmosphere is an example of a global commons

D. Global carbon dioxide concentrations in the atmosphere have increased since the Industrial Revolution

E. Global climate change results from ozone layer depletion

17. Which one of the following statements regarding carbon taxes is false?

A. Carbon taxes would have the most impact on coal prices

B. Carbon taxes would reduce negative environmental externalities

C. Carbon taxes would not set the exact level of carbon emissions

D. The effect of a carbon tax depends on the elasticity of demand for fossil fuels

E. A revenue-neutral carbon tax implies an increase in income taxes and/or other taxes

18. The elasticity of demand for carbon-based fuel sources is ...

A. Low in the short term but higher in the long term

B. High in the short term but lower in the long term

C. High in both the long and short term

D. Low in both the long and short term

E. Zero in the short term and positive in the long term

19. Which one of the following statements is false?

A. The World Bank currently screens all projects for potential environmental impacts.

B. World Bank loans are often coupled with grants from other organizations

C. World Bank funding for environmental projects has steadily increased since 1994

D. World Bank projects include both a âbrownâ and a âgreenâ agenda

E. World Bank loans must eventually be repaid

20. Which one of the following statements is true?

A. Strong sustainability assumes that most resources can be substituted for one another

B. Strong sustainability is easier to achieve that weak sustainability

C. Instituting strong sustainability would require extensive government intervention in markets

D. Strong sustainability is supported by traditional economic theory

E. Strong sustainability dictates that no non-renewable resources be used

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ECON10005 Chapter Notes - Chapter 3: Central Limit Theorem, Variance, Bias Of An Estimator

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