a. To determine Test the hypothesis. Find the P -value. Explanation Given info: The Sample sizes are n 1 = 10 and n 2 = 15 with x ¯ 1 = 4.7 and x ¯ 1 = 7.8 , and σ 1 = 10 , σ 2 = 5 . The significance level is 0.05. Calculation: Step 1: The parameter of interest is the difference in means μ 1 − μ 2 . Step 2: Null hypothesis: H 0 : μ 1 = μ 2 That is, there is not difference between the two means. Step 3: Alternative hypothesis: H 1 : μ 2 ≠ μ 2 That is, there is difference between the two means. Step 4: Test statistic: Z 0 = X ¯ 1 − X ¯ 2 − Δ 0 σ 1 2 n 1 + b. To determine Explain the conclusion using a confidence interval. c. To determine Find the power of test in part (a) for a true difference in means is 3. d. To determine Find the sample size that should be used to obtain β = 0.05 .

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 10.1, Problem 1E

To determine

Test the hypothesis.

Find the P-value.

To determine

Explain the conclusion using a confidence interval.

To determine

Find the power of test in part (a) for a true difference in means is 3.

To determine

Find the sample size that should be used to obtain β=0.05.

Expert Solution & Answer

Chapter 10 Solutions

Applied Statistics and Probability for Engineers

Ch. 10.1 - 10-1. Consider the hypothesis test H0 : μ1 = μ2...Ch. 10.1 - 10-2. Consider the hypothesis test H0 : μ1 = μ2...Ch. 10.1 - Prob. 3E Ch. 10.1 - 10-4. Two machines are used for filling plastic...Ch. 10.1 - Prob. 5E Ch. 10.1 - 10-6. The burning rates of two different...Ch. 10.1 - 10-7. Two different formulations of an oxygenated...Ch. 10.1 - 10-8. A polymer is manufactured in a batch...Ch. 10.1 - 10-9. The concentration of active ingredient in a...Ch. 10.1 - 10-10. An article in Industrial Engineer...

Ch. 10.1 - 10-11. Reconsider the data from Exercise 10-10....Ch. 10.1 - 10-12. Reconsider the study described in Exercise...Ch. 10.1 - 10-13. In their book Statistical Thinking (2nd...Ch. 10.2 - 10-14. Consider the following computer...Ch. 10.2 - 10-15. Consider the computer output...Ch. 10.2 - 10-16. Consider the hypothesis test H0 : μ1 = μ2...Ch. 10.2 - 10-17. Consider the hypothesis test H0 : μ1 = μ2...Ch. 10.2 - 10-18. Consider the hypothesis test H0 : μ1 = μ2...Ch. 10.2 - 10-19. The diameter of steel rods manufactured on...Ch. 10.2 - 10-20. An article in Fire Technology investigated...Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - 10-23. In semiconductor manufacturing, wet...Ch. 10.2 - 10-24. Two suppliers manufacture a plastic gear...Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - 10-27. Two companies manufacture a rubber material...Ch. 10.2 - 10-28. The thickness of a plastic film (in mils)...Ch. 10.2 - 10-29. An article in Electronic Components and...Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - 10-33. The overall distance traveled by a golf...Ch. 10.2 - 10-34. The “spring-like effect” in a golf club...Ch. 10.2 - 10-35. Reconsider the paper towel absorbency data...Ch. 10.2 - 10-36. European scientists sampled rivers in...Ch. 10.2 - 10-37. Olympic swimmers are seeded according to...Ch. 10.2 - Prob. 38E Ch. 10.2 - 10-39. An article in Polymer Degradation and...Ch. 10.2 - 10-40. An article in Quality Engineering [2012,...Ch. 10.3 - 10-41. An electrical engineer must design a...Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 45E Ch. 10.3 - Prob. 46E Ch. 10.3 - 10-47. Another nonparametric test known as Tukey’s...Ch. 10.3 - Prob. 48E Ch. 10.4 - 10-49. Consider the shear strength experiment...Ch. 10.4 - Prob. 50E Ch. 10.4 - Prob. 51E Ch. 10.4 - Prob. 52E Ch. 10.4 - Prob. 53E Ch. 10.4 - Prob. 54E Ch. 10.4 - 10-55. Ten individuals have participated in a...Ch. 10.4 - Prob. 56E Ch. 10.4 - 10-57. An article in Neurology (1998, Vol. 50, pp....Ch. 10.4 - Prob. 58E Ch. 10.4 - Prob. 59E Ch. 10.4 - 10-60. Repeat Exercise 10-59 using the Wilcoxon...Ch. 10.4 - 10-61. Neuroscientists conducted research in a...Ch. 10.4 - Prob. 62E Ch. 10.5 - 10-63. For an F distribution, find the...Ch. 10.5 - Prob. 64E Ch. 10.5 - Prob. 65E Ch. 10.5 - 10-66. Consider the hypothesis test against ....Ch. 10.5 - 10-67. Consider the hypothesis test against ....Ch. 10.5 - Prob. 68E Ch. 10.5 - Prob. 69E Ch. 10.5 - Prob. 70E Ch. 10.5 - Prob. 71E Ch. 10.5 - 10-72. Consider the gear impact strength data in...Ch. 10.5 - Prob. 73E Ch. 10.5 - Prob. 74E Ch. 10.5 - 10-75. Reconsider the overall distance data for...Ch. 10.5 - 10-76. Reconsider the coefficient of restitution...Ch. 10.5 - Prob. 77E Ch. 10.5 - Prob. 78E Ch. 10.5 - Prob. 79E Ch. 10.5 - Prob. 80E Ch. 10.5 - Prob. 81E Ch. 10.6 - 10-82. Consider the following computer...Ch. 10.6 - Prob. 83E Ch. 10.6 - Prob. 84E Ch. 10.6 - Prob. 85E Ch. 10.6 - Prob. 86E Ch. 10.6 - Prob. 87E Ch. 10.6 - 10-88. A random sample of 500 adult residents of...Ch. 10.6 - Prob. 89E Ch. 10.6 - Prob. 90E Ch. 10.6 - Prob. 91E Ch. 10.6 - 10-92 Consider the highway speed limit data...Ch. 10 - Prob. 93SE Ch. 10 - Prob. 94SE Ch. 10 - Prob. 95SE Ch. 10 - Prob. 96SE Ch. 10 - 10-97. A liquid dietary product implies in its...Ch. 10 - Prob. 98SE Ch. 10 - Prob. 99SE Ch. 10 - Prob. 100SE Ch. 10 - Prob. 101SE Ch. 10 - 10-102. In a random sample of 200 Phoenix...Ch. 10 - 10-103. Consider the previous exercise, which...Ch. 10 - Prob. 104SE Ch. 10 - 10-105. Two machines are used to fill plastic...Ch. 10 - Prob. 106SE Ch. 10 - Prob. 107SE Ch. 10 - Prob. 108SE Ch. 10 - Prob. 109SE Ch. 10 - 10-110. An experiment was conducted to compare the...Ch. 10 - Prob. 111SE Ch. 10 - Prob. 112SE Ch. 10 - 10-113. An article in the Journal of the...Ch. 10 - Prob. 114SE Ch. 10 - Prob. 115SE Ch. 10 - Prob. 116SE Ch. 10 - Prob. 117SE Ch. 10 - Prob. 118SE Ch. 10 - Prob. 119SE Ch. 10 - Prob. 120SE Ch. 10 - Prob. 121SE Ch. 10 - Prob. 122SE Ch. 10 - Prob. 123SE Ch. 10 - Prob. 124SE

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