a. Explanation Given info: The data represents the cut-on wave lengths of 11 wafers measured. Calculation: It is assumed that the underlying distribution is normal. Step 1: Parameter of interest The parameter of interest is the true mean of cut-on wave length, μ . Step 2: Null hypothesis Null hypothesis: H 0 : μ = 6.5 Step 3: Alternative hypothesis H 1 : μ ≠ 6.5 Step 4: Test statistic The test statistic is, t 0 = x ¯ − μ 0 S n Step 5: Decision rule: If P -value ≤ α , , reject the null hypothesis H 0 . If P -value > α , fail to reject the null hypothesis H 0 . The test is to be performed at 5% level of significance. Step 6: Computations To conduct the test, values of x ¯ and S is to be obtained. Software procedure: Step by step procedure to obtain the mean and standard deviation using the MINITAB software: Choose Stat > Basic Statistics > Display Descriptive Statistics . In Variables enter the column of values x b. To determine Find the P -value for the test. c. To determine Find the sample size required to detect a true mean cut-on wavelength of 6.50 μ m with probability 95%. d. To determine Find the type II error probability if the true mean cut on wave length is 6.95 μ m .

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 9, Problem 166SE

To determine

Check whether there is evidence that the mean cut-on wavelength is not 6.50μm.

To determine

Find the P-value for the test.

To determine

Find the sample size required to detect a true mean cut-on wavelength of 6.50μm with probability 95%.

To determine

Find the type II error probability if the true mean cut on wave length is 6.95μm.

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Chapter 9, Problem 165SE

Chapter 9, Problem 167SE

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Chapter 9 Solutions

Applied Statistics and Probability for Engineers

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - 9-3. The standard deviation of critical dimension...Ch. 9.1 - 9-4. The mean pull-off force of a connector...Ch. 9.1 - 9-5. A textile fiber manufacturer is investigating...Ch. 9.1 - 9-6. Repeat Exercise 9-5 using a sample size of n...Ch. 9.1 - 9-7. In Exercise 9-5, find the boundary of the...Ch. 9.1 - 9-8. In Exercise 9-5, calculate the probability of...Ch. 9.1 - 9-9. In Exercise 9-5, calculate the P-value if the...Ch. 9.1 - 9-10. The heat evolved in calories per grain of a...

Ch. 9.1 - Prob. 11E Ch. 9.1 - 9-12. In Exercise 9-10, find the boundary of the...Ch. 9.1 - Prob. 13E Ch. 9.1 - 9-14. In Exercise 9-10, calculate the P-value if...Ch. 9.1 - 9-15. A consumer products company is formulating a...Ch. 9.1 - 9-16. Repeat Exercise 9-15 assuming that the...Ch. 9.1 - 9-17. In Exercise 9-15, find the boundary of the...Ch. 9.1 - 9-18. In Exercise 9-15, calculate the probability...Ch. 9.1 - 9-19. In Exercise 9-15, calculate the P-value if...Ch. 9.1 - 9-20. A manufacturer is interested in the output...Ch. 9.1 - 9-21. Rework Exercise 9-20 when the sample size is...Ch. 9.1 - 9-22. In Exercise 9-20, find the boundary of the...Ch. 9.1 - 9-23. In Exercise 9-20, calculate the P-value if...Ch. 9.1 - 9-24. In Exercise 9-20, calculate the probability...Ch. 9.1 - 9-25. The proportion of adults living in Tempe,...Ch. 9.1 - 9-26. The proportion of residents in Phoenix...Ch. 9.1 - 9-27. A random sample of 500 registered voters in...Ch. 9.1 - 9-28. If we plot the probability of accepting H0:...Ch. 9.1 - 9-29. A quality-control inspector is testing a...Ch. 9.1 - 9-30. In the quality-control example of Exercise...Ch. 9.2 - 9-31. State the null and alternative hypothesis in...Ch. 9.2 - 9-32. A hypothesis will be used to test that a...Ch. 9.2 - Prob. 33E Ch. 9.2 - 9-34. A hypothesis will be used to test that a...Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - 9-37. For the hypothesis test H0: µ = 5 against...Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - 9-42. The mean water temperature downstream from...Ch. 9.2 - 9-43. A manufacturer produces crankshafts for an...Ch. 9.2 - Prob. 44E Ch. 9.2 - 9-45. The life in hours of a battery is known to...Ch. 9.2 - 9-46. An engineer who is studying the tensile...Ch. 9.2 - 9-47. Supercavitation is a propulsion technology...Ch. 9.2 - 9-48. A bearing used in an automotive application...Ch. 9.2 - Prob. 49E Ch. 9.2 - 9-50. Humans are known to have a mean gestation...Ch. 9.2 - 9-51. The bacterial strain Acinetobacter has been...Ch. 9.3 - 9-52. A hypothesis will be used to test that a...Ch. 9.3 - Prob. 53E Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Prob. 56E Ch. 9.3 - Prob. 57E Ch. 9.3 - Prob. 58E Ch. 9.3 - Prob. 59E Ch. 9.3 - Prob. 60E Ch. 9.3 - Prob. 61E Ch. 9.3 - 9-62. An article in the ASCE Journal of Energy...Ch. 9.3 - 9-63. A 1992 article in the Journal of the...Ch. 9.3 - 9-64. Cloud seeding has been studied for many...Ch. 9.3 - 9-65. The sodium content of twenty 300-gram boxes...Ch. 9.3 - 9-66. Consider the baseball coefficient of...Ch. 9.3 - Prob. 67E Ch. 9.3 - 9-68. Reconsider the data from Medicine and...Ch. 9.3 - 9-69. Reconsider the tire testing experiment...Ch. 9.3 - 9-70. Reconsider the Izod impact test on PVC pipe...Ch. 9.3 - 9-71. Reconsider the television tube brightness...Ch. 9.3 - 9-72. Exercise 6-38 gave data on the heights of...Ch. 9.3 - 9-73. Exercise 6-41 describes testing golf balls...Ch. 9.3 - 9-74. Exercise 6-40 presented data on the...Ch. 9.3 - Prob. 75E Ch. 9.3 - Prob. 76E Ch. 9.4 - 9-77. Consider the test of against . What are the...Ch. 9.4 - Prob. 78E Ch. 9.4 - Prob. 79E Ch. 9.4 - Prob. 80E Ch. 9.4 - Prob. 81E Ch. 9.4 - Prob. 82E Ch. 9.4 - 9-83. The data from Medicine and Science in Sports...Ch. 9.4 - 9-84. The data from Technometrics described in...Ch. 9.4 - Prob. 85E Ch. 9.4 - 9-86. Data from an Izod impact test was described...Ch. 9.4 - 9-87. Data for tire life was described in Exercise...Ch. 9.4 - 9-88. If the standard deviation of hole diameter...Ch. 9.4 - 9-89. Recall the sugar content of the syrup in...Ch. 9.5 - 9-90. Consider the following computer output Test...Ch. 9.5 - Prob. 91E Ch. 9.5 - 9-92. Suppose that of 1000 customers surveyed, 850...Ch. 9.5 - Prob. 93E Ch. 9.5 - 9-94. A random sample of 300 circuits generated 13...Ch. 9.5 - Prob. 95E Ch. 9.5 - 9-96. A manufacturer of interocular lenses will...Ch. 9.5 - 9-97. A researcher claims that at least 10% of all...Ch. 9.5 - 9-98. An article in Fortune (September 21, 1992)...Ch. 9.5 - 9-99. The advertised claim for batteries for cell...Ch. 9.5 - 9-100. A random sample of 500 registered voters in...Ch. 9.5 - 9-101. In a random sample of 85 automobile engine...Ch. 9.5 - 9-102. A computer manufacturer ships laptop...Ch. 9.5 - 9-103. In a random sample of 500 handwritten zip...Ch. 9.5 - 9-104. Construct a 90% confidence interval for the...Ch. 9.5 - 9-105. Construct a 95% lower confidence interval...Ch. 9.7 - 9-106. Consider the following frequency table of...Ch. 9.7 - 9-107. Let X denote the number of flaws observed...Ch. 9.7 - 9-108. The number of calls arriving at a...Ch. 9.7 - 9-109. Consider the following frequency table of...Ch. 9.7 - Prob. 110E Ch. 9.7 - 9-111. A group of civil engineering students has...Ch. 9.7 - 9-112. Reconsider Exercise 6-87. The data were the...Ch. 9.8 - 9-113. The Hopkins Forest is a 2600-acre forest...Ch. 9.8 - 9-114. Did survival rate for passengers on the...Ch. 9.8 - 9-115. A company operates four machines in three...Ch. 9.8 - 9-116. Patients in a hospital are classified as...Ch. 9.8 - 9-117. Grades in a statistics course and an...Ch. 9.8 - 9-118. An experiment with artillery shells yields...Ch. 9.8 - 9-119. A study is being made of the failures of an...Ch. 9.8 - Prob. 120E Ch. 9.8 - Prob. 121E Ch. 9.9 - 9-122. Ten samples were taken from a plating bath...Ch. 9.9 - 9-123. The titanium content in an aircraft-grade...Ch. 9.9 - 9-124. The impurity level (in ppm) is routinely...Ch. 9.9 - 9-125. Consider the margarine fat content data in...Ch. 9.9 - 9-126. Consider the compressive strength data in...Ch. 9.9 - 9-127. An inspector are measured the diameter of a...Ch. 9.9 - 9-128. A new type of tip can be used in a Rockwell...Ch. 9.9 - 9-129. A primer paint can be used on aluminum...Ch. 9.10 - Prob. 130E Ch. 9.10 - Prob. 131E Ch. 9.10 - 9-132. The mean breaking strength of a ceramic...Ch. 9.10 - Prob. 133E Ch. 9.10 - Prob. 134E Ch. 9.10 - Prob. 135E Ch. 9.10 - Prob. 136E Ch. 9.10 - Prob. 137E Ch. 9 - Prob. 138SE Ch. 9 - Prob. 139SE Ch. 9 - Prob. 140SE Ch. 9 - Prob. 141SE Ch. 9 - 9-142. An article in Fire Technology [“An...Ch. 9 - Prob. 143SE Ch. 9 - 9-144. A manufacturer of semiconductor devices...Ch. 9 - Prob. 145SE Ch. 9 - Prob. 146SE Ch. 9 - 9-147. Suppose that in Exercise 9-146. the...Ch. 9 - Prob. 148SE Ch. 9 - Prob. 149SE Ch. 9 - Prob. 150SE Ch. 9 - Prob. 151SE Ch. 9 - Prob. 152SE Ch. 9 - Prob. 153SE Ch. 9 - Prob. 154SE Ch. 9 - Prob. 155SE Ch. 9 - 9-156. Consider the spot weld shear strength data...Ch. 9 - Prob. 157SE Ch. 9 - Prob. 158SE Ch. 9 - Prob. 159SE Ch. 9 - Prob. 160SE Ch. 9 - Prob. 161SE Ch. 9 - Prob. 162SE Ch. 9 - Prob. 163SE Ch. 9 - Prob. 164SE Ch. 9 - Prob. 165SE Ch. 9 - Prob. 166SE Ch. 9 - Prob. 167SE Ch. 9 - Prob. 168SE Ch. 9 - Prob. 169SE Ch. 9 - Prob. 170SE Ch. 9 - Prob. 171SE Ch. 9 - Prob. 172SE Ch. 9 - 9-167. Consider the fatty acid measurements for...Ch. 9 - Prob. 174SE Ch. 9 - 9-175. Let X1, X2, ..., Xn be a sample from an...

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Check whether there is evidence that the mean cut-on wavelength is not 6.50 μ m .

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Check whether there is evidence that the mean cut-on wavelength is not 6.50μm.

Find the P-value for the test.

Find the sample size required to detect a true mean cut-on wavelength of 6.50μm with probability 95%.

Find the type II error probability if the true mean cut on wave length is 6.95μm.

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Chapter 9 Solutions