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Statistics Problems

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1. What type of statistical comparison can be made when observed statistics are proportions and the sample size is greater than 30?
a. t-test
b. z-test
d. f-test

2. With a normal distribution, we know that
a. Approximately 95% of all observations will fall within one standard deviation of the mean.
b. Approximately 99% of all observations will fall within one standard deviation of the mean.
c. Approximately 95% of all observations will fall within two standard deviations of the mean.
d. Approximately 99% of all observations will fall within two standard deviations of the mean.

3. A parameter represents
a. the geographical boundary of a population.
b. certain characteristics of a random sample.
c. fixed characteristics of a population.
d. fixed characteristics of a nonprobability sample.

4. The standardized normal distribution
a. is symmetrical about its mean
b. has a standard deviation of 1
c. has an infinite number of cases (continuous distribution)
d. all of the above

5. A confidence interval estimates is
a. only as good as its weakest link
b. not really a statistical calculation
c. a specified range of numbers within which a population mean
is expected to lie
d. the same thing as the mode

6. Which type of scale assumes an arbitrary zero point?
a. ratio
b. median
c. interval
d. nominal
e. ordinal

7. Code words, letters, or numbers used by security and intelligence organizations to form secret codes are examples of what type of scales?

a. nominal
b. ordinal
c. interval
d. ratio
e. continuous
8. The question, "How would you judge the price and quality of this product?" is
a. double-barreled
b. leading
c. contain s an implied alternative
d. contains an implied assumption
e. forces generalization on the part of the respondent.

9. Which of the following about interval scales is FALSE?
a. An interval scale exhibits the property of order.
b. Absolute magnitudes cannot be compared using an interval scale because the zero point is established arbitrarily.
c. The number of years the respondent has lived at a particular address is an example of an interval scale.
d. a and b.
e. a, b, and c.

Find the total proportion of the area under the normal curve for the following statements. Include four decimal places. Show your work.

10. below a z score of -1.45 ________

11. above a z score of +1.73 ________

12. between the mean and a z score of +2.11 ________

13. The probability density of the standardized normal distribution is
a. 1.0
b. 0
c. 3.0
d. 2.3
14. Indicate the type of scale is used to answer the following question. What is your job title:
_____ assistant professor; _____ associate professor; _____ full professor.
1. nominal
2. ordinal
3. interval
4. ratio

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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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