a. Explanation Given info: The data represents the observations collected on the number of errors in a string of 1000 bits of a communication channel. Calculation: Step 1: Parameter of interest The variable of interest is the form of the distribution for the number of errors in a string of 1000 bits. Step 2: Null hypothesis H 0 : The form of the distribution is binomial. Step 3: Alternative hypothesis H 1 : The form of the distribution is not binomial. Step 4: Test statistic The test statistic is, χ 0 2 = ∑ i = 1 k ( O i − E i ) 2 E i The hypothesized distribution χ 0 2 has approximately a chi-square distribution with k − p − 1 degrees of freedom. Degrees of freedom: Here, the random variable X has 4 categories. Thus, the degrees of freedom for the test is, d f = k − p − 1 = 4 − 1 − 1 = 2 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 The sample mean is estimated as shown below: p ^ sample = sample mean n The frequency values are obtained by counting the number of times each observation occurred and is given in the following table: x i f i x i f i 0 3 0 1 7 7 2 4 8 3 5 15 4 1 4 5 0 0 Total 20 34 The sample mean is calculated as shown below: Sample mean = ∑ x i f i ∑ f i = 34 20 = 1.7 Thus, the sample mean is, p ^ sample = sample mean n = 1.7 1000 = 0.0017 The expected frequencies are obtained for binomial distribution with n = 1000 and p = 0.0017 . Software procedure: Step by step procedure to obtain the probability values using the MINITAB software: Choose Calc> Probability Distribution > Binomial distribution b. To determine Find the P -value for the test.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 9, Problem 155SE

To determine

Check whether a binomial distribution is an appropriate model for the data and to perform goodness of fit test procedure at 5% level of significance.

To determine

Find the P-value for the test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 154SE

Chapter 9, Problem 156SE

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...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman

MATLAB: An Introduction with Applications

Statistics

ISBN:9781119256830

Author:Amos Gilat

Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...

Statistics

ISBN:9781305251809

Author:Jay L. Devore

Publisher:Cengage Learning

Statistics for The Behavioral Sciences (MindTap C...

Statistics

ISBN:9781305504912

Author:Frederick J Gravetter, Larry B. Wallnau

Publisher:Cengage Learning

Elementary Statistics: Picturing the World (7th E...

Statistics

ISBN:9780134683416

Author:Ron Larson, Betsy Farber

Publisher:PEARSON

The Basic Practice of Statistics

Statistics

ISBN:9781319042578

Author:David S. Moore, William I. Notz, Michael A. Fligner

Publisher:W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:9781319013387

Author:David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:W. H. Freeman

SEE MORE TEXTBOOKS

Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY

Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY

Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY

Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License