Explanation Given info: The information is based on strategies used by the wait staff at restaurants to increase their tips. The percentage of bill for the waitress introduced herself and not introduced is given below: Introduction: x ¯ = 22.63 , s 1 = 7.82 , m = 50 . No introduction: y ¯ = 14.15 , s 2 = 6.10 , n = 50 Calculation: Here, μ 1 represents the average tips for the introduction of the wait staff and μ 2 represents the average tips for the no introduction of the wait staff. Assume that parameter θ = μ 1 − 1.5 μ 2 and level of significance α = 0.05 . The test hypotheses are, Null hypothesis: H 0 : θ ≤ 0 That is, the true average tips for the introduction of the wait staff is at most the average tips for the no introduction of the wait staff. Alternative hypothesis: H a : θ > 0 That is, the true average tips for the introduction of the wait staff is greater than the average tips for the no introduction of the wait staff. The estimate of θ is obtained as given below: Here E ( μ 1 ) = X ¯ , E ( μ 2 ) = 1.5 Y ¯ E ( θ ^ ) = ( μ 1 − 1.5 μ 2 ) = ( μ 1 ) − 1.5 ( μ 2 ) = E ( X ¯ ) − 1.5 E ( Y ¯ ) θ ^ = X ¯ − 1.5 Y ¯ The variance of θ ^ is obtained as shown below: V ( θ ^ ) = V ( X ¯ ) + V ( 1.5 Y ¯ ) σ θ ^ 2 = σ 1 2 m + 1.5 2 σ 2 2 n The standard deviation is obtained by: σ θ ^ = σ 1 2 m + 1.5 2 σ 2 2 n The standard deviation in terms of sample: σ θ ^ = s 1 2 m + 1.5 2 s 2 2 n Substitute s 1 = 7.82 , s 2 = 6

Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th

9th Edition

ISBN: 9798214004020

Author: Jay L. Devore

Publisher: Cengage Learning US

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Chapter 9, Problem 87SE

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Chapter 9, Problem 86SE

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Chapter 9 Solutions

Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th

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Chapter 9 Solutions