ECON 010 Chapter Notes - Chapter 8: Interval Estimation, Point Estimation, Standard Deviation

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brownantelope443

13 Jul 2018

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In the previous chapter we saw how a point estimate can be derived to estimate a population parameter. The sample mean x was used as the point estimator for the population mean, . However, the point estimator is unlikely to provide the exact value of the true population parameter. Thus it is necessary to calculate an interval estimate (margin of error) to provide information about how close the point estimate is to the true value of the population parameter. The sampling distributions we discussed in the previous chapter will play a key role in finding these interval estimates. Interval estimate of a population mean: is known. In order to develop an interval estimate of a population mean either the population standard deviation, or the sample standard deviation, s must be used to compute the margin of error. In most cases, the true population standard deviation, is not known and s is used.

Related Questions

The USA Today reports that the average expenditure on Valentine's Day is $100.89.Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 30 female consumers was $68.64, and the average expenditure in a sample survey of 40 male consumers was 135.67. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20.

a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

b.At 99% confidence, what is the Margin of Error?

c.Develop a 99%confidence interval for the difference between two population means.

lavendermule614

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

ECON 010 Chapter Notes - Chapter 8: Interval Estimation, Point Estimation, Standard Deviation

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