Q&A Hero

Q: In utility analysis, a utility curve that shows a rapid increase in utility for initial amounts of money followed by a gradual leveling off for larger amounts of money is appropriate for a risk-seeking decision maker.

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The best alternative (course of action) for the EKA manufacturing company, using the maximax criterion, is alternative 1.

Q: When we use the expected monetary value criterion, the expected payoff equals the actual payoff that will be realized.

Q: The expected monetary value criterion is best used when a large number of similar decisions will be made.

Q: The maximax criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum (best) possible payoff.

Q: The maximax criterion is preferred by pessimistic decision makers.

Q: A decision maker's expected utility is based upon his/her attitude toward risk.

Q: When the maximin criterion is used, the decision maker assumes that for any alternative action, the state of nature with the maximum payoff will take place.

Q: The maximin criterion is preferred by optimistic decision makers.

Q: Maximax is a criterion used when making decisions under uncertainty.

Q: Maximin is a criterion used when making decisions under certainty.

Q: A tire manufacturer needs to choose the production level for the coming month (high vs. low). The level of production largely depends on the level of demand. For this situation, the level of demand (high, medium, low) is the state of nature.

Q: The maximax criterion finds the worst possible payoff for each alternative and then chooses the alternative that yields the maximum of those worst possible payoffs.

Q: A set of potential future conditions that will have an effect on the results of a decision is called the states of nature.

Q: The maximin criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum payoff.

Q: An investor is looking at three possible investments: growth stock, blue chip stock, or municipal bonds. The investment performance will vary depending on the investment market condition of bull (market rising), flat, or bear (market falling). The investment return for each investment for the corresponding market conditions is given below. Which investment would the investor select if using the maximax criterion?

Q: An investor is looking at three possible investments: growth stock, blue chip stock, or municipal bonds. The investment performance will vary depending on the investment market condition of bull (market rising), flat, or bear (market falling). The investment return for each investment for the corresponding market conditions is given below. Which investment would the investor select if using the maximin criterion?

Q: A company wants to add a new product to its existing line of products. There are two similar candidate products, A and B. The demand for the new product could be high, medium, or low, with probabilities of .25, .5, and .25, respectively. The demand and the corresponding profit for each product are shown below. Which product should the company select based on the expected monetary value criterion?

Q: A decision maker has prepared the following decision tree. There are two main decision alternatives (A and B). The probabilities for the states of nature are as follows: P(H) = .3, P(M) = .5, P(L) = .2, P(S) = .25, P(P) = .75. Calculate the highest expected profit for the decision maker and determine which of the two alternatives he/she should select.

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is not defective. Given that the inspected item is not defective, determine which alternative action the quality control manager should choose.

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. Bf the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is defective. Given that the inspected item is defective, determine which alternative action the quality control manager should choose.

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature.

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is not defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature.

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What is the maximum amount that the quality control manager would be willing to pay for perfect information?

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to the expected monetary value criterion?

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to the maximin criterion?

Q: The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S1), 50 percent chance that the lot is fair quality (S2), and 20 percent chance that the lot is good quality (S3). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars. What alternative action should be selected according to the maximax criterion?

Q: A pharmaceutical company manufacturing flu test kits wants to determine the probability of a teenager not having the flu when the test results indicate that they do. It is estimated that the probability of positive test for flu among potential users of the kit is 10 percent. According to the company laboratory test results, 1 out of 100 noninfected teenagers tested as having the flu (false positive). On the other hand, 1 out of 200 teenagers with the flu tested as not having the active virus (false negative). A teenager has just used the flu test kit manufactured by the company and the results showed she does not have the flu. What is the probability that she has the flu?

Q: A pharmaceutical company manufacturing flu test kits wants to determine the probability of a teenager not having the flu when the test results indicate that they do. It is estimated that the probability of positive test for flu among potential users of the kit is 10 percent. According to the company laboratory test results, 1 out of 100 noninfected teenagers tested as having the flu (false positive). On the other hand, 1 out of 200 teenagers with the flu tested as not having the active virus (false negative). A teenager has just used the flu test kit manufactured by the company and the results showed she has the flu. What is the probability that she does not have the flu?

Q: An automobile insurance company is in the process of reviewing its policies. The company is considering increasing the premium charged to drivers under 25. According to company records, 35 percent of the insured drivers are under the age of 25. Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident. On the other hand, only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident. What is the probability that an insured driver of any age will be involved in an accident?

Q: An automobile insurance company is in the process of reviewing its policies. The company is considering increasing the premium charged to drivers under 25. According to company records, 35 percent of the insured drivers are under the age of 25. Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident. On the other hand, only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident. An accident has just been reported. What is the probability that the insured driver is under the age of 25?

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. Based on this information, the prior probabilities have been revised. If the weather conditions are favorable, P(S1) = .4286, P(S2) = .5357, and P(S3) = .0357; and if the weather conditions are poor, P(S1) = .1364, P(S2) = .6818, and P(S3) = .1818. It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44. Determine the expected value of sample information. What is the maximum amount that the company is willing to pay for the weather information and the additional analysis?

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. Based on this information, the prior probabilities have been revised. If the weather conditions are favorable, P(S1) = .4286, P(S2) = .5357, and P(S3) = .0357; and if the weather conditions are poor, P(S1) = .1364, P(S2) = .6818, and P(S3) = .1818. It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44. Carry out a preposterior analysis and, using the revised probabilities, determine (1) the expected monetary value when the weather conditions are favorable and (2) the expected monetary value when the weather conditions are poor.

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. If the weather conditions are poor, determine which manufacturing strategy the company should implement.

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. If the weather conditions are favorable, determine which manufacturing strategy the company should implement.

Q: Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (SI) represent the levels of demand for the company products. S1, S2, and S3 characterize high, medium, and low demand, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. Construct the revised probability table for poor weather conditions, and find the probability of high demand given that the weather conditions are poor.

Q: For eight randomly selected states, the following table lists the per capita beer consumption (in gallons) and the per capita wine consumption (in gallons).Beer Wine32.2 3.129.4 4.435.3 2.334.9 1.729.9 1.428.7 1.226.8 1.241.4 3.0Test H0: ps = 0 vs. HA: ps > 0 for the relationship between beer consumption and wine consumption at the state level at = .05.A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: For eight randomly selected states, the following table lists the per capita beer consumption (in gallons) and the per capita wine consumption (in gallons).Beer Wine32.2 3.129.4 4.435.3 2.334.9 1.729.9 1.428.7 1.226.8 1.241.4 3.0Calculate the rank correlation coefficient when beer consumption = x, and wine consumption = y.A. rs = .506B. rs = .703C. rs = .711D. rs = .494

Q: A readability analysis is conducted to determine how easy four different newspapers are to read for the average citizen. The sample scores are below.A B C D50 59 45 6250 60 48 6453 63 51 6858 65 54 7059 67 55 72At the = .01 level of significance, test the claim that the four newspapers have the same readability level.A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: A readability analysis is conducted to determine how easy four different newspapers are to read for the average citizen. The sample scores are below.A B C D50 59 45 6250 60 48 6453 63 51 6858 65 54 7059 67 55 72Calculate H.A. 20.00B. 14.95C. 11.345D. 12.06

Q: A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly selected students were tested.Before After100 106111 11293 9592 9099 10785 100117 126110 10598 110At = .05, test to determine if the coaching increases test scores.A. Reject the null hypothesisB. Do not reject the null hypothesis

Q: A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly selected students were tested.Before After100 106111 11293 9592 9099 10785 100117 126110 10598 110What is the rejection point T0 for = .05?A. 8B. 6C. 4D. 6.5

Q: A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly selected students were tested.Before After100 106111 11293 9592 9099 10785 100117 126110 10598 110Calculate T- and T+.A. 44, 1B. 38.5, 6.5C. 45.5, 2.5D. 32.5, 12.5

Q: A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly selected students were tested.Before After100 106111 11293 9592 9099 10785 100117 126110 10598 110Set up the null hypothesis for the claim that the coaching is effective in increasing scores.A. H0: The probability distribution of test scores before and after the coaching is identical.B. H0: The probability distribution of test scores before the coaching is shifted to the left of the probability distribution of the test scores after the coaching.C. H0: The probability distribution of test scores before the coaching is shifted to the right of the probability distribution of the test scores after the coaching.D. H0: The probability distribution of test scores before the coaching is shifted to the left or right of the probability distribution of the test scores after the coaching.

Q: An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers.Internet Local Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 On the average, can we conclude that Internet purchases are significantly less than local store purchases? Test at = .05A. Reject the null hypothesis; Internet purchases are less than local stores.B. Do not reject the null hypothesis; there is not enough evidence to show that Internet purchases are less than local stores.

Q: An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers.Internet Local Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 What is the test statistic T?A. 111B. 130C. 60D. 120

Q: An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers.Internet Local Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 Calculate the value of TI and TE.A. 60, 130B. 130, 60C. 55, 135D. 135, 55

Q: An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers.Internet Local Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 Set up the alternative hypothesis for the claim that buying over the Internet (I) is cheaper than buying from the local stores (E).A. HA: DI is shifted to the right of DE.B. HA: DI is shifted to the left or right of DE.C. HA: DI is shifted to the left of DE.D. HA: DI is identical to DE.

Q: Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00On average, can we conclude that the machines distribute the same amount? Test at α = .05.A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00What is the test statistic T?A. 116B. 94C. 131D. 79

Q: Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00Calculate the values of TA and TB.A. 116, 94B. 131, 79C. 55, 105D. 105, 55

Q: Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine.Machine A Machine B6.10 5.995.95 6.015.98 5.986.01 5.966.00 6.085.95 5.896.02 6.016.04 6.005.99 5.976.06 6.00What is the appropriate null hypothesis for the claim that they distribute the same amount of coffee?A. H0: DA DBB. H0: DA = DBC. H0: DA DBD. H0: DA DB

Q: A local real estate agent claims that the median selling price of homes in a major midwestern city is more than $200,000. Suppose a random sample of 100 homes sold in the last six months is taken and 53 sold for over $200,000. Using = .01, test the real estate agent's claim. What do you conclude about the selling prices of the homes?A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: A local real estate agent claims that the median selling price of homes in a major midwestern city is more than $200,000. Suppose a random sample of 100 homes sold in the last six months is taken and 53 sold for over $200,000. State the null hypothesis to test the claim. Assume that the population of selling prices is not normally distributed.A. H0: Md $200,000B. H0: Md $200,000C. H0: Md $200,000D. H0: Md > $200,000

Q: A manufacturer of cell phone batteries claims that the median life of a battery is more than 40 hours. Suppose a random sample of 75 batteries finds that 32 have a life of more than 40 hours. Using = .05, can we conclude that the battery life is more than 40 hours?A. Reject the null hypothesis; z = 1.38.B. Do not reject the null hypothesis; z = 1.38.C. Reject the null hypothesis; z = -1.38.D. Do not reject the null hypothesis; z = -1.38.

Q: A manufacturer of cell phone batteries claims that the median life of a battery is more than 40 hours. Suppose a random sample of 75 batteries finds that 32 have a life of more than 40 hours. State the null hypothesis to test the claim. Assume that the population of all battery lives is not normally distributed.A. H0: Md 40B. H0: Md 40C. H0: Md > 40D. H0: Md 40

Q: We have the following sample data: .980, 1.01, .970, .990, 1.00, 1.00, .980, .970, .980, and .999. Run a sign test on H0: Md = 1.00 with a 2-sided alternative at = .05. What do you conclude?A. Reject the null hypothesis; p value = .0352.B. Do not reject the null hypothesis; p value = .004.C. Reject the null hypothesis; p value = .004.D. Do not reject the null hypothesis; p value = .0352.

Q: A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam. The scores on both exams are given below. It is established that both test scores have highly nonnormal distributions.Student Written exam score Oral exam score1 60 552 72 783 33 604 89 875 61 796 65 827 25 418 80 589 92 9510 48 6411 65 70At = .05, can we conclude that the oral exam scores are higher than the written exam scores?A. Do not reject the null hypothesis.B. Reject the null hypothesis.

Q: A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam. The scores on both exams are given below. It is established that both test scores have highly nonnormal distributions.Student Written exam score Oral exam score1 60 552 72 783 33 604 89 875 61 796 65 827 25 418 80 589 92 9510 48 64The medical examination board wants to know if the oral exam scores are higher than the written exam scores. State the appropriate null hypothesis for this problem.A. H0: The probability distribution of written exam scores is identical to the probability distribution of oral exam scores.B. H0:The probability distribution of written exam scores is shifted to the left of the probability distribution of oral exam scores.C. H0:The probability distribution of written exam scores is shifted to the right of the probability distribution of oral exam scores.D. H0:The probability distribution of written exam scores is shifted to the left or right of the probability distribution of oral exam scores.

Q: An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment. He randomly selected six countries to determine if there is a significant relationship between debt and unemployment rate. In the following table, debt figures for the 6 countries are given in billions of dollars and the corresponding unemployment rate is given in percentages. He also discovered that both the distribution of debt and the distribution of unemployment rate were highly skewed. Use Spearman's rank correlation and determine if there is a significant correlation between debt and unemployment rate. Show the rank correlation.Country Debt Unemployment Rate1 1 52 3 53 5 84 1 45 6 86 6 12A. rs = .914, reject the null hypothesis.B. rs = .886, do not reject the null hypothesis.C. rs = .886, reject the null hypothesis.D. rs = .914, do not reject the null hypothesis.

Q: In an effort to improve productivity in its factory, a firm recently instituted a training program for its workers. One of the work crews consisted of 14 workers. Seven workers from this crew were selected at random to attend the training course. All seven workers selected successfully completed the training course. The remaining seven workers served as a control group and did not attend the training course. Three months after the training course, a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity. A rank of 14 indicates the most productive employee in the crew, while a rank of 1 indicates the least productive worker.Trained Ranks Untrained Ranks7 612 214 94 38 113 510 11At = .05, can it be concluded that training was beneficial in improving productivity?A. Reject the null hypothesis; training is beneficial.B. Do not reject the null hypothesis; we cannot determine if the training makes a difference.

Q: In an effort to improve productivity in its factory, a firm recently instituted a training program for its workers. One of the work crews consisted of 14 workers. Seven workers from this crew were selected at random to attend the training course. All seven workers selected successfully completed the training course. The remaining seven workers served as a control group and did not attend the training course. Three months after the training course, a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity. A rank of 14 indicates the most productive employee in the crew, while a rank of 1 indicates the least productive worker.Trained Ranks Untrained Ranks7 612 214 94 38 113 510 11State the null hypothesis for this problem.A. H0: DT DUB. H0: DT DUC. H0: DT DUD. H0: DT > DU

Q: Three years ago, a major hotel chain purchased a large number of heating and air-conditioning units from three major manufacturers, A, B, and C. The accounting department of the hotel chain kept records on their repair and replacement costs over the last three years. The manager of the purchasing department randomly selected six brand A, seven brand B, and six brand C heating and air-conditioning unit records. The repair and replacement costs in dollars are summarized in the following table. At = .05, can we conclude that there is a significant difference in repair costs among the three brands?Brand A Brand B Brand C$80 $100 $140$250 $170 $280$150 $430 $100$70 $290 $100$220 $370 $340$300 $420 $250$350 A. Reject the null hypothesis.B. Fail to reject the null hypothesis.

Q: In a manufacturing facility producing fasteners, a foreman suspects that the diameter of the bolts produced by his first-shift workers is greater than the diameter of the bolts produced by his second-shift workers. He takes a sample of five bolts from the first-shift and a sample of four bolts from the second-shift and measures the diameters in inches. Below are the results from five first-shift and four second-shift observations. The bolt diameter measurements are not normally distributed.Bolt Diameter (inches)1st shift 2nd shift2.01 1.802.25 1.951.98 2.302.05 2.002.03 At = .05, can we conclude that his suspicion is correct?A. Reject the null hypothesis, the diameter is greater for 1st shift versus 2nd shift.B. Do not reject the null hypothesis, there is no evidence that the diameters differ by shift.

Q: Two NFL scouts are in the process of recruiting seven college senior football players (receivers). After a careful review and evaluation, both scouts ranked the seven receivers in terms of their professional career prospects. The rankings are given below.Player (Receiver) Rankings of Scout 1 Rankings of Scout 21 3 32 2 13 1 24 4 65 5 46 7 77 6 5At = .05, does it appear that the two scouts have similar opinions about the professional football career prospects of the seven players (positive correlation vs. no correlation)?A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: Two NFL scouts are in the process of recruiting seven college senior football players (receivers). After a careful review and evaluation, both scouts ranked the seven receivers in terms of their professional career prospects. If we want to determine whether the two scouts have similar opinions about the professional football career prospects of the seven players, state the null hypothesis.A. H0: s 0B. H0: s 0C. H0: s 0D. H0: s = 0

Q: A cholesterol test was given to ten heart patients with high cholesterol levels. The same ten heart patients are then given a new cholesterol-reducing drug for six months. Before the patients begin taking the drug, they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined. After taking the drug for six months, the same patients are given a cholesterol test again. The cholesterol levels before and after taking the drug are given below. The cholesterol level readings are not normally distributed. At = .05, test to determine if the drug is helpful in reducing cholesterol levels. Cholesterol levelPatient Before After1 210 2052 208 2043 185 1864 215 2075 192 1936 218 2147 170 1788 196 1909 220 21210 215 204A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: A cholesterol test was given to ten heart patients with high cholesterol levels. The same ten heart patients are then given a new cholesterol-reducing drug for six months. Before the patients begin taking the drug, they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined. After taking the drug for six months, the same patients are given a cholesterol test again. The pharmaceutical company that manufactures the drug wants to determine if the drug is helpful in reducing cholesterol levels. The cholesterol level readings are not normally distributed. State the alternative hypothesis for this problem. A. The probability distribution of cholesterol readings of patients before and after the trials is identical. B. The probability distribution of cholesterol readings at the end of six months has shifted to the left of the probability distribution of cholesterol readings at the beginning of the trials. C. The probability distribution of cholesterol readings at the end of six months has shifted to the right of the probability distribution of cholesterol readings at the beginning of the trials. D. The probability distribution of cholesterol readings of patients at the end of six months has shifted to the right or left of the probability distribution of cholesterol readings at the beginning of the trials.

Q: A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selected 8 repair records associated with brand A and 8 repair records associated with brand B. The repair times (in minutes) for both samples are given below. The distribution of repair times for both brand A and brand B is highly skewed.Brand A 160 159 171 155 136 128 173 143Brand B 125 160 140 131 119 123 135 134On average, can it be concluded that the repair time for brand A is significantly higher than the repair time for brand B?Test at = .05.A. Reject the null hypothesis.B. Fail to reject the null hypothesis.

Q: A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selected 8 repair records associated with brand A and 8 repair records associated with brand B. The repair times (in minutes) for both samples are given below. The distribution of repair times for both brand A and brand B is highly skewed.Brand A 160 159 171 155 136 128 173 143Brand B 125 160 140 131 119 123 135 134What is the appropriate alternative hypothesis for this problem?A. HA: DA is shifted to the left or right of DBB. HA: DA is shifted to the right of DBC. HA: DA is shifted to the left of DBD. HA: DA is equal to DB

Q: An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use. Currently each programming language is used by approximately 1/3 of the company's programmers. The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer. All three populations have highly skewed distributions with extreme outliers.The rank sum values for each of the programming groups are T1 = 23, T2 = 48, and T3 = 49. At = .05, does the median time required to program a simple task differ between the three different programming languages?A. H = 4.34, reject the null hypothesis.B. H = 4.34, do not reject the null hypothesis.C. H = 5.99, reject the null hypothesis.D. H = 5.99, do not reject the null hypothesis.

Q: An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use. Currently each programming language is used by approximately 1/3 of the programmers employed by the company. The director of the programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer. It is known that all three populations have highly skewed distributions with extreme outliers. Calculate the value of Ti (rank sum) for Program B.Program A Program B Program C9 14 1210 11 167 8 76 9 108 15 13A. 23B. 48C. 49D. 57

Q: Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.Assume that the population of starting salaries in marketing is not normally distributed. The p value is found to be .0547. Using = .10, can we conclude that the starting salaries increased in the last five years?A. YesB. No

Q: Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.Assume that the population of starting salaries in marketing is not normally distributed. Using = .05, can we conclude that the starting salaries increased in the last five years?A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.State the alternative hypothesis. Assume that the population of starting salaries in marketing is not normally distributed.A. HA: Md < 34,000B. HA: Md > 34,000C. HA: Md 34,000D. HA: Md = 34,000

Q: The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acme showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115.Assume the population of PSI readings is highly nonnormal. The EPA wants to determine if there is significant evidence to conclude that Acme air is dirtier than the stipulated clean air standards. The test is conducted at = .05 and the p value is found to be .254. Based on this result, provide a one-sentence managerial conclusion.A. Acme air is dirtier than the EPA stipulated clean air standards.B. We cannot conclude that Acme air is dirtier than the EPA stipulated clean air standards.C. Acme air is better than the EPA stipulated clean air standards.D. Acme air meets the EPA stipulated clean air standards.

Q: The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acme showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115. Assume the population of PSI readings is highly nonnormal. Is there significant evidence to conclude that Acme air is dirtier than the stipulated clean air standards?A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acme showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115. The EPA wants to test to determine if Acme air is dirtier than the stipulated clean air standards. Assume the population of PSI readings is highly nonnormal and state the null hypothesis.A. H0: Md 100B. H0: Md 100C. H0: Md 100D. H0: Md > 100

Q: Wax-com Electronics Inc. claims that a certain circuit board has a median operating life of less than 20,000 hours. A random sample of 25 such circuit boards showed 8 circuit boards failing before 20,000 hours and 17 circuit boards failing after 20,000 hours. Assume the useful life of the circuit board is not normally distributed. At = .05, can it be concluded that the sample contradicts the company's claim? Assume the useful life of the circuit board is not normally distributed.A. Reject the null hypothesis.B. Do not reject the null hypothesis.

Q: Wax-com Electronics Inc. claims that a certain circuit board has a median operating life of less than 20,000 hours. A random sample of 25 such circuit boards showed 8 circuit boards failing before 20,000 hours and 17 circuit boards failing after 20,000 hours. Assume the useful life of the circuit board is not normally distributed and state the null hypothesis.A. H0: Md 20,000B. H0: Md 20,000C. H0: Md < 20,000D. H0: Md 20,000