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Statistics And Probability With Applications For Engineers And Scientists Using MINITAB R And JMP 2nd Edition Irwin Guttman, Kalanka P. Jayalath, Bhisham C. Gupta - Solutions
1. With trade, the production possibilities for two nations liea. outside their consumption possibilities.b. inside their consumption possibilities.c. at a point equal to the world production possibilities curve.d. none of the above.
11. The following table summarizes the supply and the demand for euros:Using the above table:a. Graph the supply and demand curves for euros.b. Determine the equilibrium exchange rate.c. Determine what the effect of a fi xed exchange rate at $0.10 per euro would be.
10. For each of the following situations, indicate the direction of the shift in the supply curve or the demand curve for dollars, the factor causing the change, and the resulting movement of the equilibrium exchange rate for the dollar in terms of foreign currency:a. American-made cars become more
9. Discuss this statement: “Because each nation’s balance of payments equals zero, it follows that there is actually no signifi cance to a balance of payments defi cit or surplus.”
8. Do you support a constitutional amendment to prohibit the federal government from imposing any trade barriers, such as tariffs and quotas, except in case of war or national emergency?Why or why not?
5. Suppose the United States passed a law stating that we would not purchase imports from any country that imposed any trade restrictions on our exports. Who would benefi t and who would lose from such retaliation?
3. Consider this statement: “The principles of specialization and trade according to comparative advantage among nations also apply to states in the United States.” Do you agree or disagree? Explain.
2. Bill can paint either two walls or one window frame in one hour. In the same time, Frank can paint either three walls or two window frames.To minimize the time spent painting, who should specialize in painting walls, and who should specialize in painting window frames?
1. The countries of Alpha and Beta produce diamonds and pearls. The production possibilities schedule below describes their potential output in tons per year:Using the data in the table, answer the following questions:a. What is the opportunity cost of diamonds for each country?b. What is the
15. As shown in Exhibit 11, if people behave according to rational expectations theory, an increase in the aggregate demand curve from AD1 to AD2 will causea. labor to adjust nominal wages sluggishly.b. the aggregate supply curve to remain at SRAS1.c. the price level to eventually rise from 100 to
14. As shown in Exhibit 11, if people behave according to rational expectations theory, an increase in the aggregate demand curve from AD1 to AD2 will cause the economy to movea. directly from E1 to E3 and then remain at E3.b. directly from E1 to E2 and then remain at E2.c. from E1 to E2 initially
13. As shown in Exhibit 11, if people behave according to adaptive expectations theory, an increase in the aggregate demand curve from AD1 to AD2 will cause the price level to movea. directly from 100 to 110 and then remain at 110.b. directly from 100 to 105 and then remain at 105.c. from 100 to
12. Which of the following government policies is an incomes policy?a. A reduction in welfare expendituresb. The publication of a list of guidelines suggesting maximum wage and price increasesc. An increase in the money supplyd. All of the above
10. Suppose the government shown in Exhibit 10 uses contractionary monetary policy to reduce infl ation from 9 to 6 percent. If people have rational expectations, thena. the economy will remain stuck at point E1.b. the natural rate will permanently increase to 8 percent.c. unemployment will rise to
9. Suppose the government shown in Exhibit 10 uses contractionary monetary policy to reduce infl ation from 9 to 6 percent. If people have adaptive expectations, thena. the economy will remain stuck at point E1.b. the natural rate will permanently increase to 8 percent.c. unemployment will rise to
6. The conclusion of adaptive expectations theory is that expansionary monetary and fi scal policies intended to reduce the unemployment rate area. effective in the long run.b. effective in the short run.c. unnecessary and cause infl ation in the long run.d. necessary and reduce infl ation in the
5. Adaptive expectations theorya. argues that the best indicator of the future is recent information.b. underestimates infl ation when it is accelerating.c. overestimates infl ation when it is slowing down.d. does none of the above.e. does all of the above.
4. According to the natural rate hypothesis,a. the Phillips curve is quite fl at, so a large reduction in employment can be achieved without infl ation.b. workers adapt their wage demands to infl ation only after a considerable time lag.c. the Phillips curve is vertical in the long run at full
3. Since the 1970s, thea. Phillips curve has not been stable.b. infl ation rate and the unemployment rate have been about equal.c. Phillips curve has proven to be a reliable model to guide public policy.d. relationship between the infl ation rate and the unemployment rate moved in a
2. A diffi culty in using the Phillips curve as a policy menu isa. that the natural rate of unemployment does not exist.b. that the curve does not remain in one position.c. deciding between monetary and fi scal policies.d. that Democrats choose one point on the curve and Republicans choose another
1. The Phillips curve depicts the relationship between thea. unemployment rate and the change in GDP.b. infl ation rate and the interest rate.c. level of investment spending and the interest rate.d. infl ation rate and the unemployment rate.
9. Based on rational expectations theory, what happens to the infl ation rate and the unemployment rate in the following situations?a. Initially, the economy is operating at the natural unemployment rate of 4 percent, and the infl ation rate is also 4 percent.People correctly anticipate that an
8. Use Exhibit 8 to answer the questions below.a. Which points represent the natural unemployment rate?b. Which points represent an unemployment rate below the natural unemployment rate?c. Which points represent an unemployment rate above the natural unemployment rate?d. Explain points A and D on
5. According to adaptive expectations, what happens to the infl ation rate and the unemployment rate in the following situations?a. Initially, the economy is operating at the natural rate of 6 percent unemployment.The anticipated rate of infl ation is 6 percent, and the actual rate is also 6
3. What happened in the 1970s and early 1980s to cast doubt on the Phillips curve?
2. What were the infl ation rate and the unemployment rate last year? Do these rates lie on a Phillips curve?
1. What is a Phillips curve? Assuming the economy’s aggregate supply curve is stable, how would an increase in aggregate demand affect the unemployment rate and the infl ation rate?
6. Assume the economy is experiencing an infl ationary gap. Keynesian economists would believe thata. wages will remain infl exible.b. the federal government should decrease spending to shift the aggregate demand curve leftward.c. the Federal Reserve should lower the interest rate.d. the federal
5. Assume the economy is in short-run equilibrium at a real GDP above its potential real GDP. According to Keynesian theory, which of the following policies should be followed?a. The Federal Reserve should use open market operations and buy U.S. government securities.b. The Federal Reserve should
4. Assume the economy is operating at a real GDP below full-employment real GDP. Keynesian economists would prescribe which of the following policies?a. Noninterventionistb. Fixed rulec. Contractionaryd. Expansionary
3. Assuming the economy is in a recession, classical economists predict thata. wages will remain fi xed.b. monetary policy will sell government securities.c. higher wages will shift the short-run aggregate supply curve leftward.d. lower wages will shift the short-run aggregate supply curve
2. Assume the economy is in short-run equilibrium at a real GDP below its potential real GDP. According to classical self-correction theory, which of the following policies should be followed?a. The Federal Reserve should increase the money supply.b. The federal government should increase
1. Assume the economy is experiencing a recessionary gap. Classical economists would support which of the following policies?a. Contractionaryb. Expansionaryc. Noninterventionistd. Fixed wage
15. The Monetarist Transmission Mechanism through which monetary policy affects the price level, real GDP, and employment depends on thea. indirect impact of changes on the interest rate.b. indirect impact of changes on profi t expectations.c. direct impact of changes in fi scal policy on aggregate
14. In Exhibit 13, if the Fed believes the economy is at AD3, how might it engineer a decline in the price level?a. By decreasing the money supply, the interest rate falls, investment rises, and aggregate demand falls, causing the price level to fall.b. By decreasing the money supply, the interest
13. In Exhibit 13, a move from MS1 to MS2a. increases the money supply, causing the interest rate to rise from i2 to i1.b. increases the money supply, causing the interest rate to fall from i1 to i2.c. decreases the money supply, causing the interest rate to rise from i2 to i1.d. decreases the
12. Beginning from an equilibrium at E2 in Exhibit 12, a decrease in the money supply from $600 billion to $400 billion causes people toa. sell bonds and drive the price of bonds down.b. buy bonds and drive the price of bonds up.c. buy bonds and drive the price of bonds down.d. sell bonds and drive
11. Starting from an equilibrium at E1 in Exhibit 12, a rightward shift of the money supply curve from MS1 to MS2 would cause an excessa. demand for money, leading people to sell bonds.b. supply of money, leading people to buy bonds.c. supply of money, leading people to sell bonds.d. demand for
10. Keynesians reject the infl uence of monetary policy on the economy. One argument supporting this Keynesian view is that thea. money demand curve is horizontal at any interest rate.b. aggregate demand curve is nearly fl at.c. investment demand curve is nearly vertical.d. money demand curve is
9. Which of the following is not an issue in the Keynesian-monetarist debate?a. The importance of monetary versus fi scal policyb. The importance of a change in the money supplyc. The importance of the crowding-out effectd. All of the above
8. The V in the equation of exchange represents thea. variation in the GDP.b. variation in the CPI.c. variation in real GDP.d. average number of times per year a dollar is spent on fi nal goods and services.
7. Based on the equation of exchange, the money supply in the economy is calculated asa. M 5 V/PQ.b. M 5 V(PQ).c. MV 5 PQ.d. M 5 PQ 2 V.
6. Using the aggregate supply and demand model, assume the economy is in equilibrium on the intermediate portion of the aggregate supply curve. A decrease in the money supply will decrease the price level anda. lower both the interest rate and real GDP.b. raise both the interest rate and real
5. Assume the demand for money curve is fi xed and the Fed increases the money supply. The result is that the price of bondsa. rises.b. remains unchanged.c. falls.d. does none of the above.
4. Assume the demand for money curve is fi xed and the Fed decreases the money supply. The result is a temporarya. excess quantity of money demanded.b. excess quantity of money supplied.c. increase in the price of bonds.d. increase in the demand for bonds.
3. Assume the demand for money curve is stationary and the Fed increases the money supply. The result is that peoplea. increase the supply of bonds, thus driving up the interest rate.b. increase the supply of bonds, thus driving down the interest rate.c. increase the demand for bonds, thus driving
2. A decrease in the interest rate, other things being equal, causes a (an)a. upward movement along the demand curve for money.b. downward movement along the demand curve for money.c. rightward shift of the demand curve for money.d. leftward shift of the demand curve for money.
1. Keynes gave which of the following as a motive for people holding money?a. Transactions demandb. Speculative demandc. Precautionary demandd. All of the above
12. Why is the shape of the aggregate supply curve important to the Keynesian-monetarist controversy? (Hint: Review Exhibit 6 in the chapter on aggregate demand and supply.)
11. Suppose the investment demand curve is a vertical line. Would the Keynesian or the monetarist view of the impact of monetary policy on investment spending be correct?
8. Exhibit 6 shows the monetarist monetary policy transmission mechanism. Assume the economy is in a recession. At each arrow, identify a reason why the transmission process could fail.
7. What is the quantity theory of money, and what does each term in the equation represent?
6. “A monetarist investigator might say that the sewer fl ow of 6,000 gallons an hour consisted of an average of 200 gallons in the sewer at any one time with a complete turnover of the water 30 times every hour.”2 Interpret this statement using the equation of exchange.
5. Assume you are the chair of the Federal Reserve Board of Governors and the condition of the economy is as shown in Exhibit 5.Assume you are a Keynesian, and start at point E1 in the money market and the product market. State the likely direction of change in the price level, real GDP, and
4. Using the demand and supply schedule for money shown in Exhibit 10, do the following:a. Graph the demand for and the supply of money curves.b. Determine the equilibrium interest rate.c. Suppose the Fed increases the money supply by $100 billion. Show the effect in your graph, and describe the
3. Suppose a bond pays annual interest of $80.Compute the interest rate per year that a bondholder can earn if the bond has a face value of $800, $1,000, and $2,000. State the conclusion drawn from your calculations.
2. What are the basic motives for the transactions demand, precautionary demand, and speculative demand? Explain how these three demands are combined in a graph to show the total demand for money.
1. How much money do you keep in cash or checkable deposits on a typical day? Under the following conditions, would you increase or decrease your demand for money? Also identify whether the condition affects your transactions demand, precautionary demand, or speculative demand.a. Your salary
15. If all banks in the system shown in Exhibit 6 were identical to Tucker National Bank, the money multiplier for the system would bea. 4.b. 5.c. 10.d. 25.
12. Assume all banks in the system are identical to Best National Bank in Exhibit 5. A $1,000 open market sale by the Fed woulda. expand the money supply by $1,000.b. expand the money supply by $15,000.c. contract the money supply by $1,000.d. contract the money supply by $5,000.
10. Suppose Brad Jones deposits $1,000 in the bank shown in Exhibit 5. The result would bea. a $200 increase in excess reserves.b. a $200 increase in required reserves.c. a $1,200 increase in required reserves.d. zero change in required reserves.
9. If the bank in Exhibit 5 received $100,000 in new deposits, its addition to required reserves would bea. $10,000.b. $20,000.c. $30,000.d. $40,000.
7. The cost to a member bank of borrowing from the Federal Reserve is measured by thea. reserve requirement.b. price of securities in the open market.c. discount rate.d. yield on government bonds.
6. In a simplifi ed banking system in which all banks are subject to a 20 percent required reserve ratio, a $1,000 open market purchase by the Fed would cause the money supply toa. increase by $100.b. decrease by $200.c. decrease by $5,000.d. increase by $5,000.
5. In a simplifi ed banking system in which all banks are subject to a 25 percent required reserve ratio, a $1,000 open market sale by the Fed would cause the money supply toa. increase by $1,000.b. decrease by $1,000.c. decrease by $4,000.d. increase by $4,000.
4. If an increase of $100 in excess reserves in a simplifi ed banking system can lead to a total expansion in bank deposits of $400, the required reserve ratio must bea. 40 percent.b. 400 percent.c. 25 percent.d. 4 percent.e. 2.5 percent.
3. The Best National Bank operates with a 10 percent required reserve ratio. One day a depositor withdraws $400 from his or her checking account at the bank. As a result, the bank’s excess reservesa. fall by $400.b. fall by $360.c. rise by $40.d. rise by $400.
2. Assume a simplifi ed banking system in which all banks are subject to a uniform required reserve ratio of 30 percent and checkable deposits are the only form of money. A bank that receives a new deposit of $10,000 is able to extend new loans up to a maximum ofa. $3,000.b. $7,000.c. $10,000.d.
1. If a bank has total deposits of $100,000 with$10,000 set aside to meet reserve requirements of the Fed, its required reserve ratio isa. $10,000.b. 10 percent.c. 0.1 percent.d. 1 percent.
49. Referring to Problem 5 of Section 8.7, find a 99% confidence interval for the difference between the percentages of persons who favor a nuclear plant in their state. Compare the confidence intervals you obtained here to the one you obtained in Problem 5 of Section 8.7 and comment on the effect
48. Repeat Problem 4 of Section 8.7, using 98% and 99% confidence levels.
47. Referring to Problem 3 of Section 8.7, find a 99% confidence interval for the difference in proportions of the population favoring Brand X before and after the advertising campaign. Comment on your result.
46. Referring to Problem 2 of Section 8.7, find 90% and 95% confidence intervals for p, the probability of obtaining a head when this coin is tossed.Review Practice Problems 351
45. Referring to Problem 1 of Section 8.7, find a 99% confidence interval for p, the proportion of people in the population wearing glasses.
44. Repeat Problem 36, assuming that the two populations are normally distributed with unequal variances.
43. Two textile mills are manufacturing a type of utility rope. A consumer group wants to test the tensile strength of the rope manufactured by these mills. A random sample of 10 pieces of rope manufactured by mill I results in a sample mean of ¯X1 = 850 psi and a sample standard deviation of S1 =
42. Suppose in Problem 37 that it had been agreed to take equal sample sizes from the two populations. What size samples should be selected so that we can be 99% confident that the margin of error in estimating the difference of two population means is no more than two points? Use the sample
41. Referring to Problem 40, find by how much the sample size increases or decreases if we are willing to increase the margin of error from 0.025 to 0.05 with the same probability of 0.95.
40. Referring to Problem 38, how large a sample should be taken in order to be confident with probability 95% that the margin of error to estimate the fraction p of defective computer chips is 0.025?
39. A company with two car-repair centers in Orange County, California, is interested in estimating the percentage of car owners who are very happy with the service they received at each center. In a random sample of 120 car owners who have their cars serviced at service center I, 72 are quite
38. A semiconductor company wants to estimate the fraction p of defective computer chips it produces. Suppose that a random sample of 900 chips has 18 defective chips.Find a point estimate of p. Next, find a 95% confidence interval for the proportion p of defective chips, and also find a one-sided
37. At a certain university, the Electrical Engineering faculty decides to teach a course on robot intelligence using two different methods, one an existing method and the other a method using new strategies. The faculty randomly selects two sections of students who are scheduled to take this
36. Two samples of sizes n1 = 16 and n2 = 25 pieces of wool yarn are randomly taken from the production of two spindles and tested for tensile strength. These tests produce the following data:Sample I: 12.28 8.54 11.31 9.06 10.75 10.96 12.12 8.14 10.75 9.55 9.56 11.00 9.10 9.91 10.08 9.54 Sample
35. A recent study shows that the average annual incomes of cardiologists and gastroenterologists based on random samples of 100 and 121 are $295,000 and $305,000, respectively.Furthermore, these samples yield sample standard deviations of $10,600 and$12,800, respectively. Determine a 98%
34. Two types of copper wires used in manufacturing electrical cables are being tested for their tensile strength. From previous studies, it is known that the tensile strengths of these wires are distributed with unknown means μ1 and μ2 but known standard deviations σ1 = 6.0 psi and σ2 = 8.5
33. In a study of diameters of ball bearings manufactured by a newly installed machine, a random sample of 64 ball bearings is taken, yielding a sample mean of 12mm and a sample standard deviation of 0.6 mm. Compute a 99% confidence interval for the population mean μ.
32. A past study indicates that the standard deviation of hourly wages of workers in an auto industry is $4.00. A random sample of hourly wages of 49 workers yields an average of $55.00. Find (a) a point estimate of population mean wage, (b) the standard error of the point estimator calculated in
31. A manufacturing engineer wants to use the mean of a random sample of size 36 to estimate the average length of the rods being manufactured. If it is known that σ = 1.5 cm, find the margin of error at the 95% confidence level.Review Practice Problems 349
30. If (X1, . . . , Xn) is a random sample of size n from N(μ0, σ2), where μ0 is the known value of the population mean, find the maximum likelihood estimator of σ2. Is the maximum likelihood estimator unbiased or not for σ2? What is its distribution? What is its variance?
29. If (X1, . . . , Xn) is a random sample of size n from N(μ, σ2 0), where σ2 0 is the known value of the population variance, find the maximum likelihood estimator of μ. Is the maximum likelihood estimator unbiased for μ? What is the distribution of the maximum likelihood estimator?
28. A random sample of 60 voters selected at random from a large city indicate that 70%will vote for candidate A in the upcoming mayoral election. Find the 99% confidence interval for the proportion of voters supporting candidate A.
27. Nine out of 15 students polled favored the holding of a demonstration on campus against “the war.” Using technology, find 95% confidence limits for the proportion of all students favoring this proposal.
26. The athletic department of a large school randomly selects two groups of 50 students each. The first group is chosen from students who voluntarily engage in athletics, the second group is chosen from students who do not engage in athletics. Their body weights are measured with the following
25. The effectiveness of two drugs is tested on two groups of randomly selected patients with the following results (in coded units):Group 1: n1 = 75, ¯X1 = 13.540, S1 = 0.476 Group 2: n2 = 45, ¯X2 = 11.691, S2 = 0.519 Assume normality.(a) Find a 95% confidence interval for σ2 1 = σ2 2.(b) On
24. A group of 121 students of a large university are retested on entrance to give an average score of 114 with a standard deviation of 19.6. Another group of 91 students 348 8 Estimation of Population Parameters who have spent one year at this university are given the same test; they performed
23. A sample of 100 workers in one large plant took an average time of 23 minutes to complete a task, with a standard deviation of 4 minutes. In another large, but similar, plant, a sample of 100 workers took an average time of 25 minutes to complete the same task, with a standard deviation of 6
22. A sample of 500 rounds of ammunition supplied by manufacturer A yields an average muzzle velocity of 2477 ft/s, with a standard deviation of 80 ft/s. A sample of 500 rounds made by another manufacturer, manufacturer B, yields an average muzzle velocity of 2422 ft/s, with a standard deviation of
21. Two groups of judges are asked to rate the tastiness of a certain product. The results are as follows:Group 1: n1 = 121, ¯X1 = 3.6, S2 1 = 1.96 Group 2: n2 = 121, ¯X2 = 3.2, S2 2 = 3.24(a) Find a 95% confidence interval for σ2 1/σ2 2, assuming normality.(b) On the basis of the interval
20. A sample of 70 employees selected at random from the employees of a large brewery yields an average disabled time of 41.8 hours during a fiscal year, with a standard deviation of 6.4 hours. Construct a 99% confidence interval for the mean disabled time of employees at this firm.
19. The heights of 105 male students of university X chosen randomly yield an average of 68.05 inches and a sample standard deviation of 2.79 in. Find a 95% confidence interval for the mean of the heights of male students attending the (rather large) university X.
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