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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
16. Elongation measurements are made on 10 pieces of steel, five of which were treated with method A (aluminum plus calcium) and the remaining five with method B (aluminum only). It is conjectured that the addition of calcium will improve elongations by at least 1%. The results of the measurements
15. Two methods for preparing fish, A and B, are compared according to a specific scoring scheme. The claim has been made that μA > μB. The composite scores of two samples are:Method A Method B 4.05 4.18 3.31 2.35 5.04 4.35 3.39 2.59 3.45 3.88 2.24 4.48 3.57 3.02 3.93 3.93 4.23 4.56 3.37 3.43
14. Two methods were used in a study of the latent heat of fusing of ice. Both method A (an electrical method) and method B (a method of mixtures) were conducted with the specimens cooled to −0.72 ◦C. The data below represent the change in total heat from −0.72 ◦C, in calories per gram of
13. Certain measurements were made on test pieces selected from two batches B1 and B2, with the following results shown:Lot B1 0.240 0.238 0.243 0.242 0.244 0.237 Lot B2 0.185 0.190 0.192 0.186 0.188 0.190 If μ1 and μ2 are the means and σ2 1 and σ2 2 are the variances of the measurements in
12. The standard deviation S of muzzle velocities of a random sample of 16 rounds of ammunition was found to be 85 ft/s. If the “standard” value of σ for the muzzle velocity of this type of ammunition is 78 ft/s, test at the 5% level of significance the hypothesis H0: σ = 78 versus H1: σ >
11. A manufacturer claims that the diameters of rivets it produces have a standard deviation of σ = 0.05 inch. A sample of 16 rivets has a sample standard deviation of S= 0.07 in. Test at the 5% level of significance the hypothesis (assume normality):H0: σ = 0.05 versus H1: σ > 0.05
10. Suppose that a plot of land is surveyed by five student surveyors who find the following areas for the plot (in acres): 7.27, 7.24, 7.21, 7.28, 7.23. On the basis of this information, test the hypothesis that the true area of the plot is 7.23 acres or not at the 5% level of significance (assume
9. Nine determinations were made by a technician of the melting point of manganese with the following results: 1268, 1271, 1259, 1266, 1257, 1263, 1272, 1260, 1256 in (degrees centigrade). Test at the 5% level of significance the hypothesis that the results are consistent with the published value
8. Five determinations of the percentage of nickel in a prepared batch of ore produced the following results:3.25, 3.27, 3.24, 3.26, 3.24 If μ is the “true percentage of nickel in the batch”, test the hypothesis H0: μ =3.25 against the alternatives H1: μ = 3.25 at the 1% level of
7. A company is engaged in the stewed-fruit canning business. One of its brands is a medium-sized tin of cooked prunes that is advertised as containing 20 oz of prunes.The company must be sure that it packs prunes into the tins so that the mean weight is not “too much” under or over 20 oz
6. A diamond-cutting machine has been set to turn out diamonds of “0.5-karat” weight.Assume from past experience that the machine produces diamonds of weight that 432 9 Hypothesis Testing has the N(μ, 0.0036) distribution. It is important to a jewelry supply house that the weight not be too
5. A liquor company is concerned about the filling of its bottles with “too little” or “too much” liquid. A filling machine set to fill “40-oz” bottles is checked by selecting at random 10 bottles and measuring their contents. Assuming that the machine fills the bottles with quantities
4. Machines producing a particular brand of yarn are given periodic checks to help insure stable quality. A certain machine has been set in such a way that it is expected that strands of the yarn will have breaking strength of μ = 19.5 oz, with a standard deviation of σ = 1.80 oz. (It has been
3. Generalize the result in Problem 2. That is, suppose that the sampling is from N(μ, σ2 0), where σ2 0 is the known value of the variance of the population. Suppose that we need to test H0: μ = μ0 against H1: μ = μ1, where μ1 < μ0, so that the level of the test is α and γ(μ1) = 1 −
2. Suppose that in Problem 2 of Section 9.3, we need to perform a test of H0: μ = 0.25 against H1: μ = 0.2490 with size α = 0.01 and power at μ = 0.2490 of 0.99, that is,β = 0.01. What sample size is necessary to achieve this?
1. Suppose that a certain type of 40-W bulbs is standardized so that its mean life is 1500 hours and the standard deviation is 200 hours. A random sample of 36 of these bulbs from lot L having mean μ was tested and found to have an average life of 1380 hours.(a) Test at the 1% significance level
10. Generate sequentially random samples from an exponential distribution f(x) =λe−λx with λ = 10 to conduct a sequential test of the hypothesis H0: λ =10 versus H1: λ > 10 at significance level α = 0.01 and power 1 − β = 0.95 atλ = 12; that is the desired value of the probability of
9. Generate sequentially random samples from a normal population with mean μ = 12 and standard deviation σ = 2 to conduct a sequential test of the hypothesis H0: μ =20 versus H1: μ = μ1 > 20 at significance level α = 0.05 and power 1 − β = 0.95 at μ = 21; that is, the desired value of the
8. Generate sequentially random samples of size 5 from a binomial population with n = 50 and p = 0.5. Conduct a sequential test of the hypothesis H0: p = 0.5 versus H1: p = p1 > 0.50 at significance level α = 0.05 and power 1 − β = 0.90 at p = 0.52; that is the desired value of the probability
7. A recently purchased rare coin is to be used to determine whether the new owner of the coin or his assistant will buy coffee at the morning office break. They agreed to keep records of the first 45 days’ tosses to help decide whether the coin is fair.Indeed, the results are (X is the number of
6. (a) In Problem 5 above find a 95% confidence interval for σ2 1/σ2 2 (i.e., do not assume that σ2 1 = σ2 2 in this problem).(b) Use part (a) to test the assumption in Problem 5 of equal variances at the 5%level of significance, that is test H0: σ2 1 = σ2 2 versus H1: σ2 1 = σ2 2.
5. Determinations of the percentage of chlorine in a batch of polymer are to be made by two analysts, 1 and 2, to see whether they do consistent work in this environment.Based on their experience working in this laboratory, it is assumed that determinations of these analysts are distributed as
4. Referring to Problem 3 previously mentioned, find a 99% confidence interval forσ2 = Var(X) and use it to test H0: σ2 = 2 versus H1: σ2 = 2.
3. A tire manufacturer has decided to bring out a new line of snow tires, equipped with studs that are inserted at the molding stage. The decision is made to test the amount of wear per 25,000 miles of use, and a standard test is planned. The weights before and after a tire is tested are recorded,
2. Two plants are to produce certain fluorescent bulbs using new equipment. Because of the similarity to the other processes making fluorescent bulbs of different types, it is known that over wide ranges of μ1 and μ2, the distributions of the life of light bulbs from plants I and II are,
1. A new and unusual plastic is to be produced by a pilot plant project using a standard extrusion method. Because of past experience with yield using a standard extrusion method, the yields, say X, are assumed to be normally distributed as N(μ, (20)2), X measured in tons. The CEO hopes that E(X)
6. A manager in a manufacturing company wants to find if the workers’ performance varies more in one shift than the other. She takes two random samples of 20 workers, 418 9 Hypothesis Testing one sample each from each shift. Then, she observes the number of nonconforming parts produced during an
5. Two random samples from two normal populations with unknown standard deviations produced the following data:Population 1 20 18 15 24 23 20 25 14 16 14 16 24 22 16 20 15 22 16 20 20 Population 2 32 33 24 32 34 25 34 32 20 26 29 21 22 37 27 30 24 22 22 30 Test, at the 5% level of significance, the
4. Referring to Problem 10 of Section 8.4, test at the 5% level of significance the hypothesis H0: σ2 1/σ2 2 = 1 versus H1: σ2 1/σ2 2 = 1.
3. Referring to Problem 8 of Section 8.4, test at the 5% level of significance the null hypothesis H0: σ2 1/σ2 2 = 1 versus H1: σ2 1/σ2 2 = 1.
2. Referring to the data of Problem 1, test at the 5% level of significance the null hypothesis H0: σ2 1/σ2 2 = 1 versus H1: σ2 1/σ2 2 < 1.
1. Resistance measurements were made on test pieces selected from two large lots L1 and L2, with the following results shown.L1(Ω) 0.14 0.138 0.143 0.142 0.144 0.137 L2(Ω) 0.135 0.14 0.142 0.136 0.138 0.14 If μ1 and μ2 are the means, and σ2 1 and σ2 2 are the variances of resistance
6. The standard deviation S of muzzle velocities of a random sample of nine rounds of ammunition was found to be 93.2 ft/s. If the “standard” value of σ for the muzzle velocity of this type of ammunition is 70 ft/s, is the value of S significantly large at the 5% level of significance?
5. The following is the data of five independent replications of a chemical experiment:7.27 7.24 7.21 7.28 7.23 Test at the 5% level of significance the hypothesis σ2 = 0.9 against the alternatives that σ2 = 0.9.
4. Nine determinations were made by a technician of the melting point of manganese with the following results:1268 1271 1259 1266 1257 1263 1272 1260 1256 Test, at the 5% level of significance, the hypothesis σ2 = 40 against the alternativesσ2 < 40.
3. Five determinations of percent of nickel in a prepared batch of ore produced the following results:3.25 3.27 3.24 3.26 3.24 Test, at the 5% level of significance, the hypothesis σ = 0.01 against the alternativesσ > 0.01.
2. Referring to the data of Problem 1 in Section 9.4, test at the 5% level of significance the hypothesis σ = 0.4% against the alternatives σ < 0.4%.
1. A producer claims that the diameters of pins he manufactures have a standard deviation of 0.05 inch. A sample of nine pins has a sample standard deviation of 0.07 inch. Is this sample value significantly larger than the claimed value of σ at the 5%level of significance?
7. A computer-assembly company gets all its chips from two suppliers. The company knows from experience that in the past both suppliers have supplied a certain proportions of defective chips. The company wants to test alternative hypotheses: (a)supplier I supplies smaller proportion of defective
6. An urban community wishes to show that the incidence of breast cancer is higher than in a nearby rural area. If it is found that 20 of 200 adult women in the urban community have breast cancer and 10 out of 150 adult women in the rural community have breast cancer, could we conclude at the 0.05
5. A heating oil company claims that one-fifth of the homes in a large city are heated by oil. Do we have reason to doubt this claim if, in a random sample 1000 homes in this city, it is found that 136 homes are heated by oil? Use a 0.01 level of significance.
4. A dry-cleaning shop claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check the claim, the spot remover is applied to 16 randomly selected spots. If only 12 of 16 spots are removed, test the following hypotheses: (a) p = 0.70 versus p < 0.70, (b) p
3. During January, an electronics company produced 1350 printed circuits of which 146 were found to be defective. The following March, it produced 1300 circuits of which 113 were found to be defective. Assuming randomness, has the production process improved from January to March? Use α = 0.01.
2. A well-known politician claims he has 55% of the vote with him on a certain issue. A private poll of 1000 voters yields a sample proportion ˆp = 0.51. Could the well-known politician be right? State your level of significance.
1. Recall that for large n, the binomial distribution can be approximated by the normal distribution; that is for large n we may write, to good approximation, Z∼=nˆp − np np(1 − p)or Z∼=ˆp − p p(1 − p)/n∼ N(0, 1)where ˆp is the observed sample proportion. What then, for n large,
8. Hemoglobin determinations were made on two sets of 11 animals that were exposed to two different environments. Each set had 11 animals. The data obtained is given below.Set I 12.8 12.4 12.6 13.5 13.9 12.5 13.4 14.0 12.7 12.2 12.4 Set II 13.9 13.6 14.2 13.1 14.9 15.3 13.8 13.8 14.2 15.7 14.5 Test
7. Repeat Problem 3, assuming that the variances are not equal.
6. Repeat Problem 2, assuming that the variances are not equal.
5. The following data give the systolic blood pressures of 10 patients before and after their cardiologist switched them to a new drug therapy program:Before 150 156 142 162 160 144 145 153 144 164 After 133 128 131 138 131 146 137 140 148 138 Do these data provide sufficient evidence at the 5%
4. The following data give the productivity scores of 10 workers before and after a training program:Before 95 97 105 94 103 97 98 95 100 95 After 105 111 111 106 106 104 105 102 106 102 Do these data provide sufficient evidence at the 5% level of significance that the training program has an
3. An experiment to determine the viscosity of two different brands of car oil, A and B, gives the results shown below. Test the hypothesis H0: μA− μB = 0 at the 5%level of significance against the alternatives H1: μA− μB= 0. Assume normality of the two populations with equal variances.A:
2. Nicotine determinations were made on each of six standard units of tobacco at each of two laboratories, say A and B, with the results shown below: (g = grams)A : Nicotine content (g) B : Nicotine content (g)26, 24, 28, 27, 32, 30 28, 31, 23, 29, 33, 32 Test the hypothesis that the results of two
1. A machine is used to package “4-oz” boxes of a certain brand of gelatin powder. A modification is suggested to increase the speed of the operation, but there is some concern that the modified settings will cause the machine to fill the boxes with less powder than before. Accordingly, 50
6. Two random samples from two normal populations, means μ1 and μ2, and with standard deviations σ1 = 4.5 and σ2 = 6.2, respectively, produced the following data:Sample I 40 26 37 44 25 35 35 43 39 29 34 43 34 42 29 38 Sample II 51 40 29 47 43 36 47 38 40 26 26 38 37 27 34 35(a) Test at the 2%
5. Refer to Problem 10 of Section 8.4. Two different brands of an all-purpose joint compound are used in residential construction, and their drying time, in hours, are recorded. Sixteen specimens for each were selected. Recorded drying times are as shown below.Brand I 11.19 10.22 10.29 11.11 10.08
4. Refer to Problem 8 of Section 8.4. The following data give the LDL cholesterol levels of two groups I and II of young female adults. Each member of group I follow a very strict exercise regimen, whereas in group II, no one does any exercise.Group I 85 84 76 88 87 89 80 87 71 78 74 80 89 79 87 75
3. Suppose that random samples of 25 are taken from two large lots of bulbs, A and B, and that ¯XA = 1610 hours and ¯XB = 1455 hours. Assuming that the standard deviation of bulb lives is 200 hours, test at the 5% level of significance the hypothesis H0: μA− μB = 120 versus H1: μA− μB=
2. It is known from past experience that two machines, A and B, used in producing a certain type of thread have standard deviations 0.04 and 0.03, respectively. The settings of the two machines are changed, and the concern is whether they were both 9.6 Tests Concerning the Difference of Means of
1. A method for determining the percentage of iron in mixed fertilizer is available, and long experience with the method shows that its determinations are normally distributed with standard deviation of 0.12%. A company producing a certain type of fertilizer wishes to compare the findings of its
5. Suppose in Problem 6 of Section 9.3 that the population standard deviation was not known. In order to test the hypothesis under consideration, the quality control engineer decided to take a random sample of 49 rivets and measure their diameters.The data obtained are as follows:0.251 0.256 0.249
4. A customer buys most of his wine from a winery in Napa Valley in California.He wants to check if the bottle-filling machine dispenses the exact amount of wine indicated on the bottle. He took a random sample of 36 bottles and measured the 380 9 Hypothesis Testing actual amount of wine in them,
3. An aptitude test has been given over the past many years with a mean performance of 90. A group of 30 students are preparing for this test and are taught with special emphasis on remedial reading. The 30 students obtain an average of 94.2 with a sample standard deviation of 8.5. Has the remedial
2. Hourly wages of employees in a certain company have become a source of contention.An impartial arbitrator finds that industry wide hourly wages are approximately normally distributed with a mean of $11.645 per hour. The arbitrator examines the earning records of 40 workers selected at random
1. A random sample of 50 water canteens of soldiers in a desert region show an average life of 4.34 years with a standard deviation of 1.93 years. Army experience is such that canteens are known to have an average life of 4.90 years. Test the hypothesis, at the 5% level of significance, that
8. A certain process yields pieces of steel wire with population standard deviation of their breaking strength equal to 500 psi. A random sample of nine test pieces of strands from the process yields ¯X = 12, 260. If μ is the mean of the process, and assuming normality, test at the 5% level of
7. A method for determining the percent of impurity in various types of solutions is known to give determinations having a standard deviation of 0.03. Seven determinations on a certain chemical yield the values 7.18, 7.17, 7.12, 7.13, 7.14, 7.15, and 7.16. It is important that the chemical does not
6. The following data give the actual amount of beverage in sixteen “12-oz bottles”:11.92 12.16 11.67 12.13 11.62 11.44 12.47 11.56 12.24 12.44 11.46 11.50 12.15 12.59 12.02 12.03 Assuming normality, test at the 5% level of significance the hypothesis H0: μ =12 versus H1: μ = 12. Find the
5. The following data give the output voltages of a power supply:13.76 13.97 13.94 13.81 14.92 13.77 12.64 13.52 13.27 13.83 12.68 14.33 12.81 12.63 12.46 13.98 Assuming normality, test at the 5% level of significance the hypothesis H0: μ =13.5 versus H1: μ = 13.5. Find the p-value.
4. The body temperature of infants rises significantly when they develop a cold. The following data give the body temperature of 16 infants measured 12 hours after the symptoms were first detected:103 102 103 102 104 102 103 103 105 103 106 103 104 102 102 103 Assuming normality, test at the 1%
3. The following data give the total cholesterol levels of 25 young male adults who are strict vegetarians:99 97 110 110 117 91 90 120 113 120 103 115 104 90 95 98 91 93 101 94 112 108 103 120 119 Assuming normality, test at the 1% level of significance the hypothesis H0: μ =110 versus H1: μ =
2. A consumer group complains that the gas tax (in cents per gallon) levied by the federal, state, and local governments is too high. The following data give the gas tax(in cents per gallon) in 16 metropolitan areas around the country:53 42 42 52 58 42 58 38 47 43 59 45 42 49 47 47 Assuming
1. Ten determinations of the percentage of water in a certain solution yielded ¯X =0.453% and S = 0.37%. If μ is the “true” percentage of water in the solution, assuming normality, test at the 5% level of significance the hypothesis H0: μ =0.5 versus H1: μ < 0.5.
6. Referring to Problem 2, suppose a new machine was installed recently, and a random sample of 25 rivets produced yielded an average of the diameters of ¯X = 0.255. Test at the 5% level of significance:H0: μ = 0.25 versus H1: μ > 0.25. As in Problem 2, assume that the diameters of rivets
5. Refer to Problem 2. Describe the critical region in terms of ¯X , the average of the 10 diameters, for a test at level of significance of 1%, of H0: μ = 0.25 versus H1: μ =0.25. What is the power of the test at μ = 0.2490?
4. Referring to Problem 1, test at the 5% level of significance: H0: μ = 800 versus H1:μ = 800. What is the power of the test at μ = 795 and at μ = 805?
3. Referring to Problem 1, suppose that the sample taken on 100 randomly chosen days of production using the modified process yields an average of ¯X = 785 tons. Test at the 1% level of significance: H0: μ = 800 versus H1: μ < 800. What is the power of the test at μ = 790?
2. A machine used for producing “quarter inch rivets is to be checked by taking a random sample of 10 rivets and measuring their diameters. It is feared that the wear-off factor of the machine will cause it to produce rivets with diameters less than 1/4 in. Describe the critical region in terms
1. An existing process used to manufacture paint yields daily batches that have been fairly well established to be normally distributed with mean μ = 800 tons, σ = 30 tons. A modification of this process is suggested with the view of increasing production.Assume that the daily yields, using the
4. “The schools are not in the business of pleasing parents and students, and they cannot be allowed to set their own agendas. Their agendas are set by politicians, administrators, and various constituencies that hold the keys to political power. The public system is built to see to it that the
3. Suppose a national program of free housing for the elderly is paid for by a sizable increase in income taxes. Explain a tradeoff that might occur between economic security and effi ciency.
2. Explain the advantages and the disadvantages of any two of the three basic types of economic systems.
2. Why might the leader fi nd a market system inconceivable? Is it possible for economic activities not based on self-interest to take place in a market economy?
20. Which of the following would cause the U.S.dollar to depreciate against the Japanese yen?a. Greater popularity of U.S. exports in Japanb. A higher price level in Japanc. Higher real interest rates in the United Statesd. Higher incomes in the United States
19. If the dollar appreciates (becomes stronger), this causesa. the relative price of U.S. goods to increase for foreigners.b. the relative price of foreign goods to decrease for Americans.c. U.S. exports to fall and U.S. imports to rise.d. a balance of trade defi cit for the United States.e. all
18. An increase in the equilibrium price of a nation’s money could be caused by a (an)a. decrease in the supply of money curve.b. decrease in the demand for money curve.c. increase in the supply of money curve.d. increase in the quantity of money demanded.
17. Which of the following would cause a decrease in the demand for euros by those holding U.S.dollars?a. Infl ation in France, but not in the United Statesb. Infl ation in the United States, but not in Francec. An increase in the real rate of interest on investments in France above the real rate
16. Suppose the exchange rate changes so that fewer Japanese yen are required to buy a dollar. We would conclude thata. the Japanese yen has depreciated in value.b. U.S. citizens will buy fewer Japanese imports.c. Japanese will demand fewer U.S. exports.d. none of the above will occur.
15. The United Statesa. was on a fi xed exchange rate system prior to late 1971, but now is on a fl exible exchange rate system.b. has been on a fi xed exchange rate system since 1945.c. has been on a fl exible exchange rate system since 1945.d. was on a fl exible exchange rate system prior to late
14. If a Japanese radio priced at 2,000 yen can be purchased for $10, the exchange rate isa. 200 yen per dollar.b. 20 yen per dollar.c. 20 dollars per yen.d. none of the above.
13. Which of the following international accounts records the purchase and sale of fi nancial assets and real estate between the United States and other nations?a. The balance of trade accountb. The current accountc. The capital accountd. The balance of payments account
12. Which of the following international accounts records payments for exports and imports of goods, military transactions, foreign travel, investment income, and foreign gifts?a. The capital accountb. The merchandise accountc. The current accountd. The offi cial reserve account
11. The fi gure that results when goods imports are subtracted from goods exports isa. the capital account balance.b. the balance of trade.c. the current account balance.d. always less than zero.
10. The infant industry argument for protectionism is based on which of the following views?a. Foreign buyers will absorb all of the output of domestic producers in a new industry.b. The growth of an industry that is new to a nation will be too rapid unless trade restrictions are imposed.c. Firms
9. A tariff increasesa. the quantity of imports.b. the ability of foreign goods to compete with domestic goods.c. the prices of imports to domestic buyers.d. all of the above.
8. If the countries in Exhibit 13 follow the principle of comparative advantage, the United States shoulda. buy all of its potatoes from Ireland.b. buy all of its wheat from Ireland.c. buy all of its potatoes and wheat from Ireland.d. produce both potatoes and wheat and not trade with Ireland.
7. In Exhibit 13, the opportunity cost of potatoes isa. 1/2 ton of wheat in the United States and 2/3 ton of wheat in Ireland.b. 2 tons of wheat in the United States and 1 1/2 tons of wheat in Ireland.c. 16 tons of wheat in the United States and 6 tons of wheat in Ireland.d. 3 tons of wheat in the
6. In Exhibit 13, the opportunity cost of wheat isa. 1/3 ton of potatoes in the United States and 1/2 ton of potatoes in Ireland.b. 2 tons of potatoes in the United States and 1 1/2 tons of potatoes in Ireland.c. 8 tons of potatoes in the United States and 4 tons of potatoes in Ireland.d. 1/2 ton
5. In Exhibit 13, which country has the comparative advantage in the production of potatoes?a. The United States because it requires fewer resources to produce potatoesb. The United States because it has the lower opportunity cost of potatoesc. Ireland because it requires fewer resources to produce
4. According to the theory of comparative advantage, a country should produce anda. import goods in which it has an absolute advantage.b. export goods in which it has an absolute advantage.c. import goods in which it has a comparative advantage.d. export goods in which it has a comparative
3. Which of the following is true when two countries specialize according to their comparative advantage?a. It is possible to increase their total output of all goods.b. It is possible to increase their total output of some goods only if both countries are industrialized.c. One country is likely to
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