TAMU ECO 302 - The width of a confidence interval

Multiple Choices (4 Points Each)
Chapter 9
1. The width of a confidence interval will be:
A. Narrower for 99% confidence than 95% confidence
B. Wider for a sample size of 100 than for a sample size of 50
C. Narrower for 90% confidence than 95% confidence
D. Wider when the sample standard deviation (s) is small than when s is large

2. A confidence interval increases in width as
A. The level of confidence increases
B. N decreases
C. S increases
D. All of the above

3. As standard deviation increases, samples size _____________ to achieve a specified level of confidence.
A. Increases
B. Decreases
C. Remains the same

4. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.
A. Wider than
B. Narrower than
C. Equal to

5. When a confidence interval for a population proportion is constructed for a sample size and the value of p =.4, the interval is based on:
A. The Z distribution
B. The t distribution
C. A Skewed distribution
D. None of the above

6. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a variance of .09. What is the 90% confidence interval for the true mean length of the bolt?
A. 2.8355 to 3 .1645
B. 2.5065 to 3.4935
C. 2.4420 to 3.5580
D. 2.8140 to 3.1860
E. 2.9442 to 3.0558

7. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?
A. .1608 to .2392
B. .1992 to .2008
C. .1671 to .2329
D. .1485 to .2515
E. .1714 to .2286

Chapter 10
8. For a given hypothesis test, if we do not reject H₀ and H₀ is true.
A. No error has been committed
B. Type I error has been committed
C. Type II error has been committed
D. Type III error has been committed

9. If a null hypothesis is rejected at a significance level of .05, it will ______ be rejected at a significance level of .01
A. Always
B. Sometimes
C. Never

10. If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01
A. Always
B. Sometimes
C. Never

11. If a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation and the same mean) will _________ be rejected at the same significance level.
A. Always
B. Sometimes
C. Never

12. A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average more than 22 points per game. Which of the following are the appropriate hypotheses for this problem?
A. H₀: m£ 21 vs. H_a: m> 21
B. H₀: m£ 22 vs. H_a: m> 22
C. H₀: m³ 21 vs. H_a: m< 21
D. H₀:m³ 22 vs. H_a: m< 22

13. When carrying out a large sample test of H0: m = 10 vs. Ha: m > 10 by using a critical value, we reject H0 at level of significance a when the calculated test statistic is:
A. Less than z_a
B. Less than- z_a
C. Greater than z_a/2
D. Greater than z_a
E. Less than the p value

Chapter 13
14. In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) _____ have the same sign.
A. Always
B. Sometimes
C. Never

15. The least squares regression line minimizes the sum of the
A. Differences between actual and predicted Y values
B. Absolute deviations between actual and predicted Y values
C. Absolute deviations between actual and predicted X values
D. Squared differences between actual and predicted Y values
E. Squared differences between actual and predicted X values

16. The ___________ the R² and the __________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable.
A. Higher, lower
B. Lower, higher
C. Lower, lower
D. Higher, higher

17. In simple regression analysis the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the
A. Coefficient of determination
B. Slope of the regression line
C. Y intercept of the regression line
D. Correlation coefficient
E. Standard error

18. A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________ degrees of freedom total.
A. 1, 20
B. 18,19
C. 19, 20
D. 1, 19
E. 18, 20

19. The correlation coefficient may assume any value between
A. 0 and 1
B. -´ and ´
C. 0 and 8
D. -1 and 1
E. -1 and 0

Time series Forecasting
20. In simple regression analysis, if the correlation coefficient is a positive value, then
A. The Y intercept must also be a positive value
B. The coefficient of determination can be either positive or negative, depending on the value of the slope
C. The least squares regression equation could either have a positive or a negative slope
D. The slope of the regression line must also be positive
E. The standard error of estimate can either have a positive or a negative value

21. 30. A restaurant has been experiencing higher sales during the weekends of compared to the weekdays. Daily restaurant sales patterns for this restaurant over a week are an example of _________ component of time series.
A. Trend
B. Seasonal
C. Cyclical
D. Irregular

22. When using simple exponential smoothing, the value of the smoothing constant a cannot be:
A. Negative
B. Greater than zero
C. Greater than 1
D. .99
E. Both A and C