EXPLAIN THE REASON WHY USING THE AVERAGE DEVIATION AS A MEASURE OF DISPERSION IS MEANINGLESS.

11 Jun EXPLAIN THE REASON WHY USING THE AVERAGE DEVIATION AS A MEASURE OF DISPERSION IS MEANINGLESS.

Explain the reason why using the average deviation as a measure of dispersion is meaningless.

1. Explain the reason why using the average deviation as a measure of dispersion is meaningless.

a. because the sum of the deviations always equal 0

b. because the sum of the squared deviations always equal 0

c. because the sum of the absolute deviations always equal 0

d. because the sum of the absolute deviations always equal 1

2. The null hypothesis is that a process is producing no more than the maximum allowable rate of defective items. The Type II error is

a. to conclude that the process is producing too many defectives when it actually is not.

b. to conclude that the process is not producing too many defectives when it actually is.

c. to conclude that the process is not producing too many defectives when it is not.

d. to conclude that the process is producing too many defectives when it is.

3. Which of the answers in the above question imply neither a Type I nor a Type II error?

a. none of them

b. a) and b)

c. c) and d)

d. b) and c)

4. A significance level of 5% gives a lower probability of a Type I error than a significance level of 10%.

a. true

b. false

5. It is clear that no one should ever reject a null hypothesis that has a significance level of greater than 5%.

a. true

b. false

For the next five questions consider that the manager of the pepper arena wants to determine if the average amount sold per purchase during basketball games is more than the $1.32 claimed by the concessionaire. He feels that the concessionaire may be understating pepper arena’s share of concession sales. He has a consultant randomly observe the activities of the concessionaire. The average of the 75 purchases observed was $1.46 with a standard deviation of $0.32. Do these sample results support the manager’s concern? Perform the hypothesis test using alpha = .04, and use the z-distribution.

6. What is the appropriate alternate hypothesis for this hypothesis test?

a. mu does not equal 1.32

b. mu is less than 1.46

c. mu is not equal to 1.46

d. mu exceeds 1.32

e. mu is less than 1.32

7. What is the appropriate decision rule for the hypothesis test in the above problem? Reject the null hypothesis if

a. z-critical value exceeds 1.75.

b. z-critical value exceeds 2.05.

c. z-critical value is less than -2.05 or z-critical value exceeds 2.05.

d. z-critical value is less than -1.75.

e. z-critical value is less than -1.75 or z-critical value exceeds 1.75.

8. If choice (a) above were expressed as a p-value, then that the decision rule would be reject the null hypothesis if p

a. is less than 4 percent.

b. exceeds 4 percent.

c. is less than 2 percent.

d. exceeds 2 percent.

9. What is the calculated value of the z-statistic determined from the sample data?

a. -2.14

b. 3.79

c. 32.81

d. 2.14

e. -3.79

10. If the proper decision rule is reject if z-calculated value exceeds 2.05, then the null hypothesis would be rejected if which of the following choices in the above problem were calculated?

a. a) or b)

b. c) or d)

c. b) or c) or d)

d. any of them

11. A statistician performs a hypothesis test but has no preconceived idea about at what value at she should reject the null hypothesis for this one-tailed test. If her calculated Z-statistic were 1.28, she could reject the null hypothesis at a minimum p-value of

a. 5-percent.

b. 10-percent.

c. 15-percent.

d. 90-percent.

12. Consider the above problem but in this instance she has 20 observations and a calculated t-statistic of 2.00. How many degrees of freedom should she use in evaluating the calculated statistic?

a. 19

b. 20

c. 30

d. 100

13. She can reject the null hypothesis based on the t-statistic at a minimum level of

a. .005 to .01

b. .01 to .025

c. .025 to .050

d. .050 to .10

A professor gives the same exam to different sections of a statistics course. The following is the relevant data:

Class II:

N=10

X-bar = 266.44

Sigma squared = 2,467.8

Class I:

N=7

X-bar = 208.57

Sigma squared = 1,755.10

Answer the next three questions based on the data:

14. If the professor decides to test at the 5 percent significance level, he should reject the null hypothesis if

a. z-critical exceeds 1.645 and conclude that Class I is better than Class II.

b. z-critical exceeds 1.96 and conclude that Class I is better than Class II.

c. z-critical exceeds 1.645 and conclude that Class I is the same as Class II.

b. z-critical exceeds 1.96 and conclude that Class I is the same as Class II.

15. If the professor decides to test that Class I exceeds the performance of Class II by 10 points, then he is less likely to reject the null hypothesis.

a. true

b. false

16. Do you need to do any calculations to answer questions #14 & #15?

a. yes

b. no

Use the following information for the next 4 questions: From a random sample of 100 families, the least squares (regression) function is y = 50.00 + 0.210x. It estimates the monthly expenditures on food, y as a function of gross family income (x). Both x and y are in dollars.

17. If x (family income) was $840, then the monthly food expenditures in dollars is

a. $226.40

b. $168

c. $218

d. $176

18. The best interpretation of .210 is

a. A family spends 21 cents out of each dollar on food.

b. for every $1 increase in income, the family spends an additional 21 cents on food.

c. the correlation coefficient is .210 and r-squared is .21^2. (^ means a number squared).

d. for every $1 increase in income, the family spends an additional 21 cents on food plus another 50 dollars

19. A computer printout gives you a t-ratio of 1.12.

a. You cannot reject the null hypothesis of no correlation (b1 = 0) under any circumstance since this is such a low t-ratio.

b. You can reject the null hypothesis between the 10 percent and 20 percent significance level, assuming a one-tailed test.

c. You can reject the null hypothesis between the 20 and 40 percent significance level, assuming a one-tailed test.

d. You must reject the null hypothesis because of the large sample size.

20. If a family has zero income its food expenditures

a. cannot be predicted by regression.

b. would be predicted to be $50.

c. would be predicted by a modification to R-squared to account for the zero x-value.

d. would be predicted to be $0.

21. In order to evaluate if the independent (x) and dependent (y) variable in a regression are correlated, one should use _______. In order to ascertain how well the regression predicts the value of the dependent variable, one should use ________.

a. the T-ratio // R-squared

b. R-squared // the t-ratio

c. the mean of the y-observations // the mean of the x-observations

d. the mean of the x-observations // the mean of the y-observations

22. The mean household income of a certain neighborhood is $100,000 with a population standard deviation of $15,000. Based on a sample of 25 households, a 98 percent confidence interval should be calculated using the ____ distribution, and the confidence interval is from ______.

a. Z-distribution // 93,010 to 106,990.

b. T-distribution // 93,010 to 106,990.

c. Z-distribution // 92,524 to 107,476.

d. T-distribution // 92,524 to 107,476.

e. T-distribution // 92,545 to 107,455.

23. Assume you are developing a multiple regression model with 3 explanatory variables used to predict how much a college graduate will be earning annually 5 years after graduation.

a. What three variables would you include? Are they positively or negatively related to the Y-variable. Briefly explain your rationale.

b. Write out the regression equation where b0=100 and your estimated b1, b2, and b3 coefficients have been given to you by the computer. (In other words, make them up, but give them a value that others might find believable.)

c. Explain what the b1, b2 and b3 variables mean. Your explanation must be mathematically accurate but explained so that a non-economist/non-statistician can understand your explanation.

d. Make up an X1, X2, and X3 value, and show the relevant calculations to determine Y.

24. Go to.bea.gov/national/xls/gdpchg.xls”>http://www.bea.gov/national/xls/gdpchg.xls and consider the numbers in the column (third from left) labeled “GDP Percent Change Based on Current Dollars.” This can be considered a measure of economic growth.Consider the population for this exercise to be the Post WWII years (1946-2015) GDP growth where the mean = 2.9 and the standard deviation = 2.95.

a) Take the GDP numbers for any 8-year period and tell at the 1 percent significance level if the mean GDP for these years are statistically different from the 1946-2015 average.

b) Do the same exercise, but use the sample standard deviation for the 10-year period as your estimator for the population standard deviation.

Show all work. Otherwise you will receive no credit for the answer. **

** You may use Excel. In that case attach the computer printout.