1) (Chapter 10) Given The Following T-Statistics (23 Degrees Of Freedom) And P-Values (1 Tailed);

Midterm—Sample Economics 173 Name______Fall 2001 Instructor: Petry SSN______

1. Given the following t-statistics (23 degrees of freedom) and p-values (1 tailed); t-statistic: 1.7  p-value .05 t-statistic: 1.2  p-value .121 t-statistic: 2.1  p-value .023 What is the p-value for the t-statistic 1.3?

a. .141 b. .103 c. .042 d. .013 e. .461

2. When comparing the proportions of two populations, what type of test statistic is used?

a. z b. t c. F d. all of the above e. none of the above

3. Given a population standard deviation of 13, a sample mean of 40, and a confidence interval width of 10, and a critical value of 1.645, what is the sample size?

a. 4 b. 5 c. 6 d. 7 e. 8

4. If the p-value for a test is .4 then your decision is:

a. there is sufficient evidence to conclude the alternative is correct. b. there is sufficient evidence to conclude the null is correct. c. there is insufficient evidence to conclude the alternative is correct. d. there is insufficient evidence to conclude neither is correct. e. none of the above

5. Which of the following statements are equivalent? I. Alpha II. Beta III. Probability of a Type I error

0710df8db016370df0482d1d58184112.doc Page 1 of 12 IV. Probability of a Type II error V. Probability of Rejecting a true null a. I and IV b. I and III c. I and III and V d. II and V e. II and IV and V

6. The 95% confidence interval for the population average final exam score is [126.4, 195.5]. To test the claim that the average final exam score of the population is 180 at a 3% level of significance, what will be your decision?

a. reject the null – conclude it is not 180 b. fail to reject the null – insufficient evidence to conclude it is not 180 c. reject the null – conclude it is 180 d. fail to reject the null – sufficient evidence to conclude it is not 180 e. cannot decide based on the given information

7. When doing a matched pairs test with differences distributed normally and unknown population standard deviation, which is the correct test statistic? a. equal variances pooled t test for means b. unequal variances pooled t test for means c. single population means test on the difference d. none of the above e. any of the above will work

8. If you wish to know if more than 45% of the class scored above 70% on the exam, what is your null hypothosis?

a. H0: p=0.7 b. H0: p=0.45 c. H0: p>0.7 d. H0: p>0.45 e. any of the above will work

9. Suppose we are interested in whether the mean scores on the midterm for Economics 173 is below 80%. Given a p-value of .11 what is your conclusion?

a. fail to reject the null at any reasonable level of significance b. cannot determine based on the given information c. reject the null at any reasonable level of significance d. fail to reject the null only if the significance level is .01 e. reject the null only if the significance level is .01

0710df8db016370df0482d1d58184112.doc Page 2 of 12 10. Given the following list of observations: 1, 10, 34, 15, 8, 40, 90, 41, 5, 16. What proportion is above 8?

a. .4 b. .5 c. .6 d. .7 e. .8

11. Before running an equal variances pooled t-test, what test should you run to formally decide if the needed assumptions are correct?

a. F-test for variances b. t-test for variances c. z-test for variances d. no need to run a test e. eyeball test

12. A pharmaceutical company currently produces an anesthetic whose effective time is normally distributed with mean 7.4 and standard deviation 1.2. It is considering the launch of a new drug that they believe has a lower mean effective time but the same standard deviation. In a clinical study meant to test their belief, what would be the appropriate null and alternative hypothesis?

a. Ho:  > = 7.4, H1:  < 7.4

b. Ho:  > 7.4, H1:  < =7.4

c. Ho:  = 7.4, H1:   7.4

d. Ho:  < = 7.4, H1:  > 7.4

13. Irrespective of your answer in the last question suppose that you intend to do a two-sided test. You collect a sample and compute the sample mean. In order to reject the null hypothesis at a 10% level of significance, using a Z statistic of 1.645, and a sample size of 25,

a. you need the sample mean to be smaller than 7.01 b. you need the sample mean to be greater than 7.79 c. both of the above d. none of the above

14. The mean of a sample is computed to be –0.301. It has been found out that the p-value is 0.275 when testing Ho:  = 0 against the two sided alternative H1:   0. To test Ho:  = 0 against the one sided alternative H1:  < 0 at a significance level of 0.5, we will have:

a. a p-value of 0.275 and therefore reject the null hypothesis

0710df8db016370df0482d1d58184112.doc Page 3 of 12 b. a p-value of 0.138 and therefore reject the null hypothesis c. a p-value of 0.862 and therefore accept the null hypothesis d. a p-value of 0.5 and therefore the test results will be inconclusive.

15. The following table presents the summary statistics from a sample of 24 exam scores, expressed in percentages. Score

Mean 75.66667 Standard Error 1.782226 Median 73 Mode 73 Standard Deviation 8.731087 Sample Variance 76.23188 Kurtosis 0.646501 Skewness 1.303676 Range 30 Minimum 66 Maximum 96 Sum 1816 Count 24 Confidence Level(95.0%) 3.68681

In order to do a test where the null hypothesis specifies the population mean to be equal to 70,

a. the t-distribution should be used to get a test statistic equal to 3.18 b. the z-distribution should be used to get a test statistic equal to 3.18 c. not enough information is given to calculate the test statistic d. a pooled variance t-test should be used

16. Based on a 95 % confidence interval, if you tested Ho:  = 70, H1:   70, you would:

a. not be able construct the confidence interval due to lack of information. b. Accept the null hypothesis c. Reject the null hypothesis d. Reformulate a one sided hypothesis instead.

17. The pooled variance t-test is based on the following assumption(s):

a. that the two populations be independent b. that the two populations have approximately equal variances c. that both populations be normal d. all of the above

0710df8db016370df0482d1d58184112.doc Page 4 of 12 18. A truck manufacturer has two plants, one in Champaign and one in Urbana. The CEO of this company suspects that the Urbana plant is more efficient (in terms of number of trucks produced each month) than the Champaign one. Let Champaign be plant 1 and Urbana be plant 2 . Then the test should be specified as:

a. H0: 1-2 = 0, H1: 1-2  0

b. H0: 1-2 = 0, H1: 1-2 < 0

c. H0: 1-2 = 0, H1: 1-2 > 0

d. H0: 1-2 < 0, H1: 1-2 > 0

19. For the scenario described above, monthly production data was collected from both plants for a year and a pooled variance t-test was performed at the 5% significance level. The results of the test are presented below. CHAMPAIGN URBANA Mean 57.75 55.66667 Variance 5.840909091 13.15152 Observations 12 12 Pooled Variance 9.496212121 Hypothesized Mean Difference 0 df 22 t Stat 1.655995622 P(T<=t) one-tail 0.055959227 t Critical one-tail 1.717144187 P(T<=t) two-tail 0.111918455 t Critical two-tail 2.073875294

Based on the correct answer to the last question,

a. The p-value is 0.056 so we do not reject the null hypothesis b. The p-value is 0.112 so we do not reject the null hypothesis c. The p-value is 0.888 so we do not reject the null hypothesis d. The p-value is 0.944 so we do not reject the null hypothesis.

20. The test for difference in proportions between two populations uses

a. the z-distribution b. the f-distribution c. the t-distribution d. both a and b

21. Suppose a record store chain (Badidea cd’s) is running a promotion for the new Grand Funk Railroad anthology that was released last summer. Badidea cd’s would like to know whether or not the promotion that it ran was successful or not based on it’s own sales (23 stores) of the anthology before and after the promotion. In order to test this hypothesis which of the following tests should be used?

0710df8db016370df0482d1d58184112.doc Page 5 of 12 a. pooled variance t-test assuming equal variances b. pooled variance t-test assuming unequal variances c. paired sample t-test d. z test for difference in means e. z test for difference in proportions

22. Suppose two record store chains are both running a promotion for the re- release of Mike and the Mechanics Reggae Christmas album that was released last August. Badidea cd’s (23 stores) would like to know if it’s store sold a significant amount more than its competition Dave’s Unbelievable Music Bin (DUMB) (18 stores). In order to test this which of the following tests would be the most appropriate?

a. pooled variance t-test assuming equal variances b. F test for difference in variance c. z test for difference in proportions d. t-test for population mean e. paired sample t-test

23. A poll was taken recently on the UI campus asking students whether or not they support military action to solve world conflict. Suppose you believe that men and women answer this question differently. In order to test your hypothesis that men would answer “Yes, I support military action” more often that women, which of the following tests could you perform?

a. pooled variance t-test assuming equal variances b. pooled variance t-test assuming unequal variances c. paired sample t-test d. z test for difference in means e. z test for difference in proportions

24. A poll was taken recently on the UI campus asking students whether or not they support military action to solve world conflict. Suppose you believe that the percentage of students who support military action is more than half. In order to test this hypothesis which of the following tests could you perform?

a. z test for difference in proportions b. t-test for population mean c. F test for difference in variance d. z test for population proportion e. pooled variance t-test assuming equal variances

0710df8db016370df0482d1d58184112.doc Page 6 of 12 25. A professor studying “grade inflation” (the upward trend in letter grades in most college courses) believes that the upward trend in grades is accompanied by a greater uncertainty (ie wider dispersion or spread) of letter grades. To test whether or not there is more uncertainty in letter grades, which of the following tests could be performed?

a. z test for difference in proportions b. t-test for population mean c. F test for difference in variance d. z test for population proportion e. pooled variance t-test assuming equal variances

26. In the simple linear regression model, the intercept and slope coefficients are computed by minimizing,

a. SSE b. the sum of the squared discrepancies between the observed values and its conditional mean c. the sum of the squared discrepancies between the predicted values and the conditional means d. both a and b e. both b and c

Use the following Excel output to answer the following questions. (Note: some parts left blank)

SUMMARY OUTPUT

Regression Statistics Multiple R 0.164737873 R Square 0.027138567 Adjusted R Square 0.017109068 Standard Error 6.982167345 Observations 99

ANOVA df SS MS F Significance F Regression 1 131.9131721 131.9131721 2.705874543 0.103216227 Residual 97 Total 4860.727273

Coefficients Standard Error t Stat P-value Lower 95% Intercept 10.00368557 0.872243025 11.46892012 9.40437E-20 8.272525588 X Variable 1 -0.231771626 0.140898523 -1.644954268 0.103216227 -0.511416034

0710df8db016370df0482d1d58184112.doc Page 7 of 12 27. Based on the Excel output what is the value for the total degrees of freedom?

a. 99 b. 98 c. 1 d. 97 e. 0

28. Based on the Excel output what is the value of MSE?

a. 4728.81 b. 4992.64 c. 48.75 d. 356.94 e. not enough information to answer

29. Based on the Excel output what is the correct interpretation for the slope coefficient?

a. For every 1-unit change in X, the expected average change in Y is –0.23 units. b. For every 1-unit increase in X, the expected average change in Y is –0.23 units. c. For every 1-unit increase in X, the expected average change in Y is 10.00 units. d. For every –0.23 unit decrease in X, the expected average change in Y is 1 unit. e. For every 1-unit increase in Y, the expected average change in X is –0.23 units.

30. Based on the Excel output what is the value of the appropriate test statistic for testing whether or not X has a significant effect on Y?

a. 11.47 b. –1.64 c. 0.027 d. 0.103 e. none of the above

31. Calculate the mean of the following array: 20 24 29 54 65 78

a. 40 b. 45 c. 50 d. 55 e. 65

32. What is the median salary of the following array: 20 24 29 54 65 78

0710df8db016370df0482d1d58184112.doc Page 8 of 12 a. 29 b. 38 c. 41.5 d. 46.7 e. 66

33. If the distribution is symmetrical, which of the following are equivalent?

a. the mean and median b. the mode and the median c. the mean and the mode d. the mean, the mode, and the median e. none of the above

34. The range of the measurements is:

a. the difference between the smallest and largest measurements b. the test statistic as measured in Excel c. the average of all measurements d. the number of measurements e. the difference between the mean and the test statistic

35. The variance is:

a. 2 times the standard deviation b. the square root of the standard deviation c. the absolute value of the standard deviation d. the standard deviation squared e. none of the above

36. Find the variance (in years) of the following array: 3.4, 2.5, 4.1, 1.2, 2.8, 3.7

a. 1 b. 1.05 c. 1.275 d. 2.95 e. 1.075

37. Which of the following are true regarding the standard deviation:

a. can be used to compare the variability of several distributions b. make a statement about the shape of the distribution c. contains 68% of the measurements within 1 and –1 standard deviations d. contains 95% of the measurements within 2 and –2 standard deviations

0710df8db016370df0482d1d58184112.doc Page 9 of 12 e. all of the above

38. Covariance determines:

a. the strength of the linear relationship between two variables b. if there is any pattern to the way the two variables move together c. the shape of the distribution d. the size of the population being measured e. both a and b.

39. If two variables are strongly and positively correlated, the coefficient value will be close to:

a. 0 b. .5 c. –1 d. 1 e. .2

40. What is the 95% confidence interval (Z= 1.96), for a mean of 7.8, a population standard deviation of 3, and a sample of 85:

a. 7.0651, 8.5554 b. 7.1622, 8.4377 c. 6.9749, 7.8846 d. 7.2432, 8.5094 e. 7.2321, 8.6858

41. The width of the interval estimator is a function of:

a. the population standard deviation b. the sample size c. the confidence level d. all of the above e. none of the above

42. Increasing the sample size:

a. decreases the width of the interval estimator b. increases the width of the interval estimator c. changes the confidence interval d. leads to exactly the same standard deviation e. none of the above

0710df8db016370df0482d1d58184112.doc Page 10 of 12 43. What sample size is required for a machine to be precise within 1 inch with 95% confidence (Z = 1.96)? Assume population is normally distributed, with a population standard deviation of 4.

a. 120 b. 62 c. 61 d. 70 e. 59

0710df8db016370df0482d1d58184112.doc Page 11 of 12 Answer Key: 1. b 26. d 2. a 27. b 3. b 28. c 4. c 29. b 5. c 30. b 6. b 31. b 7. c 32. c 8. b 33. d 9. a 34. a 10. d 35. d 11. a 36. e 12. a 37. e 13. c 38. b 14. b 39. d 15. a 40. b 16. c 41. d 17. d 42. a 18. b 43. b 19. d 20. a 21. c 22. a 23. e 24. d 25. c

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