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Chapter 12.4, Problem 44E

Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in Exercise 15 of Section 12.2 resulted in ŷ = 7.592, sŶ = .179 when x = 40 and ŷ = 9.741, sŶ = .253 for x = 60.

  1. a. Explain why sŶ is larger when x = 60 than when x = 40.
  2. b. Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40.
  3. c. Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40.
  4. d. If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?
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I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)

Chapter 12 Solutions

Bundle: Probability and Statistics for Engineering and the Sciences, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term Courses

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