quiz_7_Chap_8_Solution - ≤ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − n...

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Qatar University, College of Engineering Probability and statistics, GENG200 Instructor: Dr. Ridha Hamila Quiz 7 (Time: 15 minutes) 3rd rd of June 2010 Name: Student ID: Question 1: The diameter of holes for a cable harness is known to have a normal distribution with σ = 0.01 inch . A random sample of size 10 yields an average diameter of 1.5045 inch. Find the 99% two-sided confidence interval on the mean whole diameter. Answer: 99% Two sided CI on the diameter cable harness holes: where x =1.5045 , σ = 0.01 , n=10 and z 0.005 = 2.58 5127 . 1 4963 . 1 10 / ) 01 . 0 ( 58 . 2 5045 . 1 10 / ) 01 . 0 ( 58 . 2 5045 . 1 / / 005 . 0 005 . 0 + + μ σ n z x n z x Question: If the sample size n is doubled, by how much is the length of the Confidence Interval (CI) on ߤ in the following equation +
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Unformatted text preview: ≤ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − n z x n z x α 2 / 2 / reduced? What happens to the length of the interval if the sample size is increased by a factor of four? Answer: If n is doubled in Eq 8-7: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ≤ ≤ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − n z x n z x 2 / 2 / ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = = n z n z n z n z 2 / 2 / 2 / 2 / 414 . 1 1 414 . 1 414 . 1 2 The interval is reduced by 0.293 or 29.3% If n is increased by a factor of 4 Eq 8-7: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = = n z n z n z n z 2 / 2 / 2 / 2 / 2 1 2 2 4 The interval is reduced by 0.5 or ½....
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