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SAV 6 - PROGRAM OCTOBER 1999 MID-TERM EXAMINATION Time: 9:30 AM – 11:30 AM BUSINESS STATISTICS Lecturer Student ID: Date: Dr. Ho Thanh Phong Name: October 22, 1999 Instructions: a. Every question has the same score. b. For True/False question, a plus for right answer and minus for wrong answer c. Discussion is strictly prohibited. Questions 1. Classifying students in a statistics course by their home town is an example of what scale of measurement? A) Nominal B) Ordinal C) Interval D) Ratio Answer: 2. A clothes store manager has sales data of trouser sizes for the last month ’s sales. Which measure of central tendency should the manager use, if the manager is interested in the most sellable size? A) mean B) median C) mode D) standard deviation E) interquartile range Answer: 3. The mean weight of three gemstones is 12 grams. The weights of two of the stones are 9 grams and 11 grams. What is the weight of the third stone? A) 16 grams B) 10 grams C) 8 grams D) 14 grams Business Statistics -1- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 E) not enough information to determine the weight of the third stone Answer: Use the following to answer question 4, 5: The following is the age distribution in a particular building: Age Number of People 0 – 10 7 10 – 20 10 20 – 30 12 30 – 40 15 40 – 50 11 50 – 60 6 60 – 70 4 70 – 80 2 4. What is the mean age of the people living in this building? A) 67.0 B) 40.0 C) 33.5 D) 28.0 E) none of the above Answer: 5. What is the median age of people living in this building? A) 32.67 B) 30 C) 32.33 D) 34 E) 15 Answer: 6. The following numbers represent the electricity bill each house in a particular area received in the past month. $64, 79, 92, 101, 113, 115, 129, 135, 138, 143, 146, 158, 163, 165, 168, 173, 174, 177, 181, 184, 187, 189, 190, 193, 196, 200, 205, 218, 231, 249 and 278. What is the 60 th percentile for these values? A) 190.2 B) 179.4 C) 181.6 D) 182.5 E) 177 Answer: 7. A class of business students received the following test scores on a standardized test: 320, 410, 440, 470, 480, 480, 490, 500, 500, 510, 510, Business Statistics -2- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 530, 530, 530, 540, 570, 600, 650, 720 and 790. How many students in this group received a score that was greater than the 75th percent of this group? A) 56 B) 5 C) 563 D) 15 E) not enough information to answer Answer: Use the following to answer questions 8, 9, 10: The following are the valuations (in thousands of dollars) of 16 randomly selected properties sold during the past year: 130 110 130 130 120 140 120 110 150 150 130 140 130 130 120 140 8. Find the mean, median, and mode of these data: Answer: Mean: , Median: , Mode: 9. Find the variance of the distribution: Answer: Variance: 10. Based on Chebyshev’ theorem, what range would you say should include at least 75% of property valuations? Answer: [ , ] The probability distribution of the number of hours the evening flight from Chicago to New York is late is found to be as follows: X P(X) 1 0.1 2 0.1 3 0.2 4 0.3 5 0.2 6 0.1 11. Find the standard deviation of the flight delay A) 2.00 B) 0.2 C) 1.4177 D) 3.7 E) none of the above Answer: Use the following to answer question 12, 13: Business Statistics -3- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 The number of bags per passenger travelling on a particular flight has the following probability distribution: X P(X) 0 0.1 1 0.3 2 0.4 3 0.1 4 0.1 12. What percentage of passengers who have more than one bag? A) 60% B) 30% C) 10% D) 90% E) 40% Answer: 13. What percentage of passengers has at least one bag? A) 60% B) 30% C) 10% D) 90% E) 40% Answer: Use the following to answer questions 14, 15: A company has a new project under way and selects five executives for a transfer from their current jobs. A report had suggested that 75% of all executives in this company would like this new job. 14. What is the probability that at least three of these five selected like their new job? A) 0.4219 B) 0.45 C) 0.25 D) 0.5781 E) 0.8965 Answer: 15. What is the probability that exactly three of the five selected like their new job? A) 0.0264 B) 0.4219 C) 0.7363 D) 0.2637 Business Statistics -4- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 E) 0.8965 Answer: 16. A new medicine has an 85% success rate. Five patients are treated with it. What is the probability that at least four are cured with this new medicine? A) 0.4437 B) 0.3915 C) 0.5220 D) 0.83521 E) none of the above Answer: 17. The arithmetic mean assumes an interval level of measurement. A) True B) False Answer: 18. Chebyshev’s Theorem states that at least 8/9 of the observations in a set will lie within 3 standard deviations of the mean. A) True B) False Answer: 19. A record of the numbers of models of each of five models of cars sold by a dealership during the past 18 months is an example of ordinal data. A) True B) False Answer: 20. A random variable is discrete if it can assume only certain values within its range. A) True B) False Answer: 21. In a binomial experiment with n= 50 trials, and the probability of success on each trial equal to 0.2, the expected value of the random variable is 40. A) True B) False Answer: 22. The probability that a standard normal random variable will have a value of ten is very close to one. A) True B) False Business Statistics -5- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 Answer: 23. The probability that a normal random variable will be within two standard deviations of its mean is approximately 0.68. A) True B) False Answer: 24. A calculator manufacturer performs a test on its calculators and finds their working life to be normally distributed, with a mean of 2150 hours and a standard deviation of 450 hours. What should the manufacturer advertise as the life of the calculators so that 90% of the calculators are covered? A) 2555 B) 1947 C) 1410 D) 1745 E) 1574 Answer: 25. Find two values symmetric around a mean of 20 such that they include an area equal to 0.75. (standard deviation = 5). A) 16.65, 23.35 B) 19.25, 20.75 C) 16.25, 23.75 D) 14.25, 25.75 E) none of the above Answer: 26. The contents of a particular bottle of shampoo marked as 150 ml are found to be 154 ml at an average, with a standard deviation of 2.5 ml. What proportion of shampoo bottles contain less than the marked quantity? Assume a normal distribution. A) 0.2192 B) 0.1096 C) 0.4452 D) 0.0548 E) none of the above Answer: 27. The IQ’s of the employees of a company are normally distributed, with a mean of 127 and a standard deviation of 11. What is the probability that the IQ of an employee selected at random will be between 120 and 130? A) 0.2389 B) 0.3453 Business Statistics -6- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 C) 0.1064 D) 0.1325 E) 0.4638 Answer: 28. The GMAT scores of students in a college are normally distributed with a mean of 520 and a standard deviation of 41. What proportion of students have a score higher than 600? A) 0.9744 B) 0.2372 C) 0.4774 D) 0.0256 E) none of the above Answer: 29. If X is a normal random variable with mean 12 and standard deviation 2, then the probability that X will exceed 16 is? A) 0.04772 B) 0.0228 C) 0.9772 D) 0 E) 1 Answer: 30. The sample standard deviation, s, is a point estimate for . A) True B) False Answer: 31. A sample size of 30 or more values is large enough for the Central Limit Theorem to be effective. A) True B) False Answer: 32. The Central Limit Theorem states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation. A) True B) False Answer: 33. In which of the following situations is the Central Limit Theorem not Business Statistics -7- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 appropriate? A) When the sample is small and the population is normal. B) When the sample is large and the population is normal. C) When the sample is large, above 30, and the population is not normal. D) When the sample is small, below 30, and the population is not normal. E) none of the above Answer: 34. The standard deviation of the average number of cassettes a college student owns is 14. What minimum sample size of students will give a sample standard deviation of at most 4? A) 12 B) 4 C) 13 D) 3 E) 18 Answer: 35. The average telephone bill in a locality is $70, with a standard deviation of $40. In a sample of 50 randomly selected phone connections, what is the probability that the sample average will exceed $75? A) 0.3106 B) 0.8694 C) 0.1894 D) 0.4483 E) none of the above Answer: 36. Which of the following statements does not refer to the Central Limit Theorem? A) The expected value of the mean of the distribution of sample means is . B) The distribution of sample means is approximately normally distributed. C) The standard deviation of the distribution of sample means is equal to . D) The Central Limit Theorem is true for any distribution, when the sample size is at least 30. E) When a non-normal population is sampled, the distribution of sample means is still normally distributed, as long as the sample size is large. Answer: 37. One way to get a narrower confidence interval, is to increase the sample size. A) True B) False Business Statistics -8- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 Answer: 38. The closer it is necessary for the sample estimate to be to the unknown population parameter, the smaller the sample size required. A) True B) False Answer: 39. A type II error is the error that is committed if the null hypothesis is rejected when in fact it is true. A) True B) False Answer: 40. When the null hypothesis is not rejected, then we can assume that the null hypothesis is certainly true. A) True B) False Answer: 41. The p-value of a hypothesis test is always less than alpha. A) True B) False Answer: 42. The p-value is the chance that you are taking of making a type I error. A) True B) False Answer: 43. The mean annual sales of a company in 36 of its sales offices over the country is $23,860,000, with a standard deviation of $2,150,000. A manager quotes the annual sales of the company to be $25,000,000. Compute the p- value to test whether the sample data provide evidence to reject the executive’s claim that the average annual sales are $25,000,000. A) 0.2726 B) 0.3637 C) 0 D) 0.0007 E) 0.0014 Answer: 44. I would like to test the null hypothesis that the population mean is 50 versus the alternative that it is not 50. My sample size is 6, and the sample mean is Business Statistics -9- Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 38 with sample standard deviation of 16. At = 0.05, I should: A) strongly reject the null hypothesis B) mildly reject the null hypothesis C) fail to reject the null hypothesis D) accept the alternative hypothesis E) there is insufficient information to determine Answer: 45. The proportion of defective items is not allowed to be over 15%. A buyer wants to test whether the proportion of defectives exceeds the allowable limit. The buyer takes a random sample of 100 items and finds that 19 are defective. State the null and alternative hypotheses for this test. A) H0: p .15, H1: p > .15 B) H0: p < .15, H1: p .15 C) H0: p = .15, H1: p .15 D) H0: p < .15, H1: p > .15 E) none of the above Answer: 46. A manufacturer claims that his tires last at least 40,000 miles. A test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles. Compute the test statistic. A) t = -0.65 B) t = 3.23 C) t = -3.23 D) t = 0.65 E) none of the above Answer: 47. Given a p-value of 0.065, and using the customary = 5%, the conclusion should be: A) accept the null hypothesis B) reject the null hypothesis C) not enough information to determine Answer: 48. A random sample of 36 items gave a sample mean of 48 and a sample standard deviation of 12. Compute the p-value to test whether or not the population mean is equal to 50. A) 0.3413 B) -0.4772 C) 0.1587 D) 0.6826 Business Statistics - 10 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 E) 0.3174 Answer: 49. I want to conduct a statistical test of whether or not the population mean is 70. My sample mean is 71, my sample standard deviation is 5, and my sample size is 100. The result is: A) not significant B) significant C) very significant D) can’t tell Answer: GOOD LUCK ! Business Statistics - 11 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 FINAL EXAMINATION Time: 9:20 AM – 11:55 AM BUSINESS STATISTICS Lecturer Student ID: Date: Name: November 25, 1999 Dr. Ho Thanh Phong Instructions: d. Every question has the same score. e. For True/False question, a plus for right answer and minus for wrong answer f. Discussion is strictly prohibited. Questions 1. The only assumption required for the paired-difference test is that the population of differences is normally distributed. a) True b) False 2. When using the t distribution to test for a difference between two population means taken from independent samples the degrees of freedom are: n 1 + n2 – 2. a) True b) False 3. The F distribution is the ratio of two chi-square random variables that are independent. a) True b) False 4. If the difference between two sample means is significant, then this is evidence that the two samples come from populations with equal means. a) True b) False Business Statistics - 12 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 5. When testing for the equality of two population means, using = 0.05 with n1 = 12 and n2 =10, the critical points are: a) +2.704 and –2.704 b) +1.96 and –1.96 c) +2.086 and –2.086 d) +1.645 and –1.645 e) none of the above Use the following to answer questions 6, 7, 8: A company made a major change in its advertising theme this year and is interested in knowing whether there is any significant increase in sales over last year. The following data is the sales in thousands for different stores over the country, and has been adjusted for inflation. Take the difference as (current year’s sales – last year’s sales). Store Last Year’s Sales Current Year’s Sales 1 183 206 2 406 528 3 388 678 4 694 601 5 274 258 6 137 170 7 33 31 8 1423 1468 6. State the null and alternative hypotheses to test the hypothesis that the change in advertising has increased sales. a) H0: D > 0, H1: D 0 b) H0: D 0, H1: D > 0 c) H0: D 0, H1: D < 0 d) H0: D = 0, H1: D > 0 e) none of the above 7. Find the critical value to test the hypothesis that the change in advertising has increased sales, using = 0.05. a) +1.645 b) +1.96 c) +2.365 d) +1.895 e) none of the above 8. Construct a 95% confidence interval for the average change in sales. a) 50.25 (2.365) (40.385) Business Statistics - 13 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 b) 50.25 (1.96) (40.385) c) 50.25 (1.895) (40.385) d) 50.25 (2.306) (40.385) e) none of the above Use the following to answer questions 9, 10: A programmer has written a software package that points out errors in programs. Previously, this was done manually. The mean number of errors the software picket out of 100 different programs was 15, with a standard deviation of 8.2. The mean number of errors picked out manually, out of 100 programs, was 13, with a standard deviation of 4.9. We want to test whether there is evidence that this software picks out more errors than checking manually does. Assume that the software is population 1 and manual checking is population 2. 9. State the null and alternative hypotheses to test whether this software does pick out more errors. 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 e) none of the above 10. Find the critical points to test whether this software does find more errors, at = 0.05. a) +1.96 b) +1.645 c) +1.282 d) +2.575 e) +2.33 11. When testing for the equality of two population proportions, the F distribution is: a) sometimes appropriate b) never appropriate c) only appropriate if both sample sizes are less than 30 d) only appropriate if at least one sample is at least 30 e) used when the two variances are not equal 12. Calculate the pooled variance for the following sample data. Sample Sample Variance Sample Size mean 40 10 12 30 12 15 a) 3.33 Business Statistics - 14 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 b) 124.64 c) 11.12 d) 34.4 e) none of the above 13. Compute the p-value for a two-tailed test of the difference in two means, with both sample sizes at least 30, if the test statistic is z = 2.50. P-value: ..................... 14. A survey was conducted to see if the proportion of men and women liking this brand of jeans differed. In a sample of 100 men and 90 women, 62 of the men liked the jeans, and 66 of the women liked the jeans. Construct a 95% confidence interval for the difference in the proportion of men and women liking these jeans. CI = [ , ] 15. In fifty different localities, the cable company gives free access to all cable channels for a weekend, as a promotional gesture. The mean proportion of customers who had the premium channels before the promotion was 20%. The mean proportion of customers who had the premium channels after the promotion was 26%. The increase significant at a = 0.05. a) True b) False 16. Your company is interested in a new method of advertising. In order to test the new method they have selected thirty-one control and thirty one experimental markets. Mean sales in the control markets were 134, 630 with a standard deviation of 5,290. Mean sales in the experimental markets were 138,780 with a standard deviation of 5,730. At the 95% confidence level you conclude that the new method is better than the old. a) True b) False 17. In an ANOVA, if the sum of squares for error is 400, the sum of squares for treatment is 180, and the total sample size for the four groups compared is 88, then the null hypothesis should not be rejected. a) True b) False 18. In an ANOVA, if: n = 130, r = 3 groups, SSE = 12490, SSTR = 13000, and using = 0.05, the decision should be to reject the null hypothesis. a) True b) False 19. In ANOVA, the sample size is 500 and seven groups are compared. The total sum of squares is 10,000. The decision should be: a) do not reject the null hypothesis Business Statistics - 15 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 b) reject the null hypothesis immediately c) not enough information given to make a decision on the null hypothesis d) mildly reject the null hypothesis e) decide that the test must be repeated since only seven groups were involved 20. In ANOVA, if the sample standard deviation within all four groups under study are approximately equal, we should: a) immediately decide not to reject the null hypothesis b) immediately reject the null hypothesis c) mildly reject the null hypothesis d) redo the test, since the standard deviation are equal e) there is not enough information to make a decision on whether to reject or not reject the null hypothesis 21. Analysis of variance is a statistical method of comparing the __________ of several populations. a) standard deviations b) variances c) means d) proportions e) none of the above 22. If the r population means are equal, then MSTR/MSE will be: a) more than 1.00 b) very close to 1.00 c) very close to 0.00 d) close to –1.00 e) a negative value between 0 and –1 Use the following to answer questions 23, 24: A watch manufacturer markets a particular model with three different straps: gold, silver and leather. The average number of sales in a week of each watch are 12, 15 and 11, respectively. An ANOVA to find whether or not the customers prefer any particular strap over the random sample, shows SSE = 1490 and SSTR = 760. 23. Compute the F test statistic for this hypothesis test. a) 0.112 b) 8.926 c) 1.96 d) 9.69 e) none of the above 24. Write the null hypothesis for this test. a) H0: not all the population means are equal b) H0: at least one of the population means is not equal to the others Business Statistics - 16 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 c) H0: 1 = 2 = 3 d) H0: 1 - 2 - 3 0 e) none of the above Use the following to answer questions 25, 26: A survey is conducted to find whether students like a particular type of music more than another: rock, pop, classical and jazz. Ratings for each class of music are collected from 50 students. SSTR = 28,590 and SST = 40,220. 25. Write the null hypothesis to test whether students like these types of music equally, or whether there is a preference. a) H0: 1 = 2 = 3 = 4 b) H0: 1 - 2 - 3 - 4 0 c) H0: s1 = s2 = s3 = s4 d) H0: at least one of the population means is different e) none of the above 26. How many degrees of freedom does the sum of squares for treatments have? a) 4 b) 3 c) 0 d) 49 e) 46 Use the following to answer questions 27, 28, 29: A marketing manager wants to determine if the average advertising spending per month of his competitors are equal or not. Data over the last six months reveals the following figures (in thousands of dollars): A: 11, 17, 27, 35, 43, 38 B: 9, 12, 27, 45, 54, 32 C: 12, 23, 28, 27, 39, 41 27. Compute SSTR for these observations. a) 4 b) 8 c) 2934 d) 16 e) none of the above 28. Calculate the F ration for the ANOVA on these observations. a) 0.05 b) 3.68 c) 0.02 d) 0.01 e) none of the above Business Statistics - 17 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 29. Find the F-value from the table to test the hypothesis that there is no difference in average spending among these three companies at = 0.05. a) 3.68 b) 19.43 c) 0.02 d) 3.29 e) none of the above Use the following to answer questions 30, 31: Standardized stock price indicators in three different countries over a week are listed below. An analyst is interested in knowing if the stock markets of these three countries are dependent on one another. The ANOVA table is given. I II III 890 900 905 899 900 900 900 887 896 905 906 928 871 893 899 910 900 934 ANOVA table Source of Sum of Degrees of Mean F Ratio Variation Squares Freedom Square Treatment 748 Error Total 3274 30. What are the degrees of freedom for the sum of squares error? a) 2 b) 15 c) 17 d) 19 e) none of the above 31. Find the T value, from the table, for the Tukey test, to determine whether or not each of the pairs of means are equal. Use = 0.05. a) 3.61 b) 11.0 c) 1.96 d) 3.67 e) none of the above Use the following to answer questions 32, 33, 34: The management of an organization wants to test to see whether the rate of turnover of employees is the same in all the departments. Samples over the last Business Statistics - 18 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 year show the following as the number of employees having left the company: Production: 5, 6, 3, 4, 6, 6 Marketing: 3, 4, 4, 4, 3, 5 Finance: 3, 3, 3, 2, 4, 5 Accounting: 2, 3, 3, 5, 6, 4 The ANOVA table is show below: Source of Sum of Degrees of Mean Square F Ratio Variation Squares Freedom Treatment Error 27.00 Total 36.00 32. State the null hypothesis for this ANOVA. a) H0: 1 - 2 - 3 0 b) H0: all of the population means are different c) H0: at least one of the population means is different d) H0: 1 = 2 = 3 e) none of the above 33. If the p-value for this ANOVA is 0.117, what is the conclusion, testing at = 0.05? a) reject the null hypothesis b) do not reject the null hypothesis c) not enough information to make a decision d) at least one of the population means is significantly different e) none of the above 34. Construct a 95% confidence interval on the population mean of the Finance department. a) 3.333 (1.725)(1.162/6) b) 3.333 (2.571)(1.162/2.449) c) 3.333 (1.725)(1.162/2.449) d) 3.333 (2.086)(1.162/2.449) e) none of the above 35. In regression analysis, every time that an insignificant and unimportant variable is added to the regression model, the R2 decreases. a) True b) False 36. In multiple regression there is no need to consider the F-test, only the t-tests are important. a) True b) False Business Statistics - 19 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 37. Using multiple regression to regress five independent variables to predict y will give the same result as five separate regressions of y versus each independent variable. a) True b) False 38. If H0: 1 = 2 = 3 … = k = 0 is rejected, then we can conclude that there is no linear relationship between y and any of the k independent variables in the model. a) True b) False 39. The Mean Square Error, or MSE, is a biased estimator for the variance of the population of errors, , denoted by 2. a) True b) False 40. The square root of the MSE is the standard error of the estimate. a) True b) False 41. The adjusted multiple coefficient of determination always increases as new variables are added to the model, just as R2 does. a) True b) False 42. When the adjust coefficient of determination decreases when a term is included in the multiple regression model, then that term should be retained in the model. a) True b) False 43. In a multiple regression analysis with n = 15 and k = 14, the computer reports R2 = 0.9999. a) this is an excellent regression b) this is a very good regression c) this is an average regression d) this is not a good regression e) not enough information to determine 44. In a multiple regression analysis, MSE = 20, n = 54, k = 3 and SST (total) = 2000. What is the R2 of the regression? a) 0.0 b) 0.01 c) 0.99 d) 1.00 e) 0.50 Business Statistics - 20 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 Use the following to answer questions 45, 46, 47: The following data gives the monthly sales (in thousands of dollars) for different advertising expenditures (also in thousands of dollars) and sales commission percentages. Sales 245 138 352 322 228 275 560 366 Advertising 16.5 18 22.3 17.4 19 20 32 18.6 Commission 10.5 2 4 3.5 4.5 1.8 9 8.5 Minitab gives the following output from a multiple regression analysis: Predictor Coef Stdev t-ratio p Constant -138.4 119.0 -1.16 0.297 Advertising 18.742 5.749 3.26 0.022 Commission 11.648 8.420 1.38 0.225 S = 72.88 R1 = 75.7% R-2 (adjusted) = 66.0% 45. What amount of sales would this model predict for advertising expenditures of 25,000 and sales commission of 8%? a) 42,333 b) 30,273.6 c) 561,734 d) 72,880 e) none of the above 46. Write the null and alternative hypotheses to test whether or not advertising expenditures and sales commission can be used to predict sales. a) H0: 1 = 2 = 0; H1: at least one coefficient is not zero b) H0: 1 2; H1: 1 = 2 c) H0: 1 and 2 are not equal to zero; H1: 1 = 2 = 0 d) H0: 1 2; H1: 1 < 2 e) none of the above 47. At the 5% level of significance, is either advertising expenditure of sales commission percentage or both significant? a) only advertising expenditures b) both are significant c) only sales commission percentage d) neither are significant e) insufficient information to determine Use the following to answer questions 48, 49, 50: Eight students are selected randomly and their present graduate GPA is compared their undergraduate GPA and scores on standardized tests. The data are show below: Present GPA 3.89 3.03 3.34 3.85 3.93 3.06 3.69 3.91 Business Statistics - 21 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 Undergr GPA 3.77 2.75 3.11 3.75 4.00 2.92 3.70 3.88 Std. Scores 700 460 550 690 720 420 670 670 The Minitab regression analysis follows: Predictor Coef Stdev t-ratio p Constant 1.1066 0.2059 5.37 0.003 Undergr GPA 0.4775 0.1630 2.93 0.033 Std. Scores 0.0013392 0.0006693 2.000 .102 Analysis of Variance Source DF SS MS F p Regression 2 1.02751 Error 5 Total 7 1.04255 48. Write the regression equation, letting undergraduate GPA be variable 1 and standard scores be variable 2. a) y = 0.4775 x1 + 0.0013392x2 b) y = 0.2059 + 0.1630x1 + 0.0006693x2 c) none of the others is correct d) y = 1.1066 + 0.4775x1 + 0.0013392x2 e) not enough information given 49. Compute R2. a) 99.4% b) 98.6% c) 20.8% d) very close to 100% e) insufficient information to determine 50. What is the relationship between R2 and the adjusted R2 for this regression model? a) both are exactly the same b) the adjusted R2 is larger than R2 c) the adjusted R2 is smaller than R2 d) both are very small e) none of the above 51. A random walk is the difference between successive values of the error term. a) True b) False 52. Prediction and forecasting are the same thing in statistical analysis. Business Statistics - 22 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 a) True b) False 53. Sales of air conditioners follow a seasonal variation. c) True d) False 54. The ratio-moving-average procedure can be used to deseasonalize data. e) True f) False 55. The following data is the total units of electricity produced in a country annually. 1981 1882 1983 1984 1985 1986 1987 1988 1989 175 179 203 222 225 259 282 292 301 Recode the years so that the average of the years is zero. Compute the slope of the trend line. a) 237.6 b) 17.3 c) 1038 d) 0.0578 e) none of the above 56. Calculate a three-day moving average for the price of stock, for Tuesday through Thursday. Day Price Monday 50.00 Tuesday 52.00 Wednesday 54.00 Thursday 54.50 Friday 60.00 a) 53.50 b) 54.10 c) 90.17 d) 54.00 e) none of the above 57. The data given below are quarterly sales for a large computer firm, in $100,000’s. Quarter Sales 1991-1 105 1991-2 110 1991-3 122 1991-4 120 1992-1 125 Business Statistics - 23 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 1992-2 135 Compute the four-quarter moving average for the first four quarters and center it at the third quarter. a) 114.25 b) 119.25 c) 116.75 d) 119.50 e) none of the above 58. The following are stock prices for a given group of stocks on the Dow Jones. Compute the forecast for day 3 using the exponential smoothing method, with w = .4. Day Original Dow Jones series 1 800 2 825 3 814 4 820 5 832 6 830 a) 800 b) 810 c) 814 d) 815 e) none of the above 59. The average credit bill of the customers of a particular organization have been as follows over the last few years: 1980 117 1981 193 1982 318 1983 367 1984 397 1985 456 1986 525 1987 591 1988 653 Estimate a linear trend line for this data. Use this trend line to predict credit balances of customers for the year 1989. a) 698.22 b) 401.89 c) 320.08 d) 721.97 e) none of the above Business Statistics - 24 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 60. A pattern in a times series model that occurs over more than a year is called a _____________ variation. 61. The sign test assumes that the pairs of values are independent. a) True b) False 62. The sign test can be used to test whether or not the population median is equal to some hypothesized value. a) True b) False 63. The following sequence contains exactly seven runs. SSESEESSSESSSE a) True b) False 64. The Mann-Whitney U test and the rank sum test are the same. a) True b) False 65. The null hypothesis for the Wilcoxon Signed-Rank Test is that the median difference between two populations is zero. a) True b) False 66. You are testing for independence using the chi-square distribution. The contingency table has two rows and four columns. The computed value of chi-square is 6.5. The p-value is: a) less than 0.005 b) between 0.005 and 0.01 c) between 0.01 and 0.05 d) between 0.05 and 0.10 e) greater than 0.10 Use the following to answer questions 67, 68: The size of the operating system of a microcomputer (in Kilobytes) has been varying as shown below, over the last eight years. 38, 41, 45, 43, 44, 42, 47, 50 67. State the null hypothesis that will test for the existence of a positive trend in this data. a) H0: p(+) 0.5 b) H0: p(+) 0.5 c) H0: p(+) 0.5 d) H0: p(+) > 0.5 e) H0: p(+) < 0.5 Business Statistics - 25 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 68. Compute the test statistic to test for a positive trend. a) T = 2 b) T = 3 c) T = 4 d) T = 8 e) T = 6 69. A computer random number generator gives the following random numbers: 5 8 5 6 9 8 7 6 6 4 3 1 1 1 0 1 1 1 0 2 How many runs are in this data? a) 20 b) 12 c) 11 d) 19 e) none of the above 70. The management of a museum wants to know if the proportions of three age groups of visitors, those under 18, those between 18 and 50, and those over 50, who buy souvenirs from the gift shop are equal. Over a particular week, the following number of people enter the museum: Visitors Number who Totals buy Under 18 108 61 169 18 – 50 137 93 230 Over 50 81 49 130 Totals 326 203 529 Compute the chi-square value to test whether the proportion of visitors buying from the museum gift shop is the same in all the age groups. a) 0.5 b) 0.15 c) 0.8927 d) 5.2 e) none of the above Use the following to answer questions 71, 72: A manager compares the profits made by two products over the last year. The following table gives the data in thousands of dollars. Month 1 2 3 4 5 6 7 8 9 10 11 12 A 23 28 55 47 22 19 15 26 37 32 46 53 B 34 27 44 56 52 43 49 34 27 41 48 39 Business Statistics - 26 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 71. Use the Mann-Whitney U test to determine whether or not there is statistical evidence that the profits over one product are greater than the profits made from the other product. Give the U statistic. Assume that A is sample 1. a) 124.5 b) 97.5 c) 175.5 d) 751.5 e) none of the above 72. Compute the E (U) for the Mann-Whitney U statistic for this data. a) 72 b) 24 c) 144 d) 66 e) none of the above 73. The only assumptions required for the Mann-Whitney U test are: a) independent samples b) random samples c) normal populations d) a and b e) a, b and c 74. The following data gives the returns on two securities, A and B, over a period of 12 months. Month 1 2 3 4 5 6 7 8 9 10 11 12 A 17 18 16 17 18 19 19 15 16 15 17 16 B 14 16 18 19 17 16 15 18 13 14 15 12 Compute the test statistic, for the Wilcoxon signed-rank test to determine whether or not there is a difference in the returns of the two securities. a) 17.5 b) 37.5 c) 12 d) 8.5 e) none of the above 75. The average life of a battery is supposed to be 250 hours of continuous operation. A random sample of 25 batteries is subject to discharge and the lifetime is recorded. The data is as follows (in hours): 214, 289, 263, 291, 240, 207, 277, 252, 285, 287, 250, 297, 268, 286, 211, 232, 282, 216, 223, 234, 219, 280, 239, 249, 230. Using the sign test to test whether there is statistical evidence to conclude that the life of the battery is less than 250 hours, find the test statistic. a) 10 Business Statistics - 27 - Dr. Ho Thanh Phong SAV 6 - PROGRAM OCTOBER 1999 b) 12 c) 13 d) 25 e) none of the above GOOD LUCK ! Business Statistics - 28 - Dr. Ho Thanh Phong