(a) Explanation Given info: The data is about the calibration constants for samples of compounds in each of four compound groups. Calculation: From the results of 16.52: The values of M S E = 0.00198 , k = 4 and n = 25 . Conduct the Tukey multiple comparison test: Step 1: The family confidence level is 0.95. Step 2: The parameters of the test is k = 4 and v = n − k = 25 − 4 = 21 From the “Appendix A: Table X values of q 0.05 ”, the q -value having the 0.05 area to its right with degrees of freedom k = 4 and v = 21 is 3.96. Step 3: Calculate the all possible endpoints of confidence interval for μ i − μ j The formula for confidence interval μ i − μ j is: ( x ¯ i − x ¯ j ) ± q α 2 ⋅ s 1 n i + 1 n j Where s = M S E The sample mean and sample sizes are: j 1 2 3 4 x ¯ j 0.1276 0.1206 0.1450 0.1248 n j 5 10 6 4 The endpoints of the confidence interval for μ 1 − μ 2 are, ( 0.1276 − 0.1206 ) ± 3.96 2 ⋅ 0.00198 ⋅ 1 5 + 1 10 = ( 0.007 ) ± ( 2.80 × 0.044 × 0.547 ) = 0.007 ± 0.0673 = ( 0.007 − 0.0673 , 0.007 + 0.0673 ) = ( − 0.0603 , 0.0743 ) The endpoints of the confidence interval for μ 1 − μ 3 are, ( 0.1276 − 0.1450 ) ± 3.96 2 ⋅ 0.00198 ⋅ 1 5 + 1 6 = ( − 0.0174 ) ± ( 2.80 × 0.044 × 0.6 ) = − 0.0174 ± 0.0739 = ( − 0.0174 − 0.0739 , − 0.0174 + 0.0739 ) = ( − 0.0913 , 0.0565 ) The endpoints of the confidence interval for μ 1 − μ 4 are, ( 0 (a) To determine To explain: Whether the data provide sufficient evidence to conclude that a difference exists in mean calibration constant among the four compound groups.

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ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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Chapter 16.4, Problem 98E

(a)

To determine

To conduct: The Tukey multiple comparison test at 95% confidence interval.

(a)

To determine

To explain: Whether the data provide sufficient evidence to conclude that a difference exists in mean calibration constant among the four compound groups.

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Chapter 16.4, Problem 97E

Chapter 16.4, Problem 99E

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= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.

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Introductory Statistics (10th Edition)

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To conduct: The Tukey multiple comparison test at 95% confidence interval.

To explain: Whether the data provide sufficient evidence to conclude that a difference exists in mean calibration constant among the four compound groups.

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