Explanation Given: The unit disk D = { ( x , y ) ∈ R 2 | x 2 + y 2 ≤ 1 } and the unit circle S 1 = { ( x , y ) ∈ R 2 | x 2 + y 2 = 1 } . The function q : R 2 → R 2 defined as q ( x , y ) = ( x , 0 ) , and the function p : D ∗ → S 1 , where D ∗ = D \ { ( 0 , 0 ) } . Draw: Let ( x , y ) ∈ D ∗ such that 0 < x < 1 and 0 < y < 1 . Then, p ∘ q | D ∗ ( x , y ) = p ( q | D ∗ ( x , y ) ) = p ( x , 0 ) = ( 1 , 0 )

3rd Edition

ISBN: 9781284056242

Author: David J. Hunter

Publisher: Jones & Bartlett Learning

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Chapter 2.3, Problem 32E

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To draw a well-labelled diagram to show that p∘q|D≠q|D∘p.

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Chapter 2.3, Problem 31E

Chapter 2.3, Problem 33E

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Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 2. Two-Sample T-Test: Compare the average sales revenue of two different regions to determine if there is a significant difference. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null) H0 = H1=

Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 3. Paired T-Test: A company implemented a training program to improve employee performance. To evaluate the effectiveness of the program, the company recorded the test scores of 25 employees before and after the training. Determine if the training program is effective in terms of scores of participants before and after the training. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional, use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting the null) H0 = H1= Conclusion:

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To draw a well-labelled diagram to show that p ∘ q | D * ≠ q | D * ∘ p .

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To draw a well-labelled diagram to show that p∘q|D≠q|D∘p.

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To draw a well-labelled diagram to show that p ∘ q | D * ≠ q | D * ∘ p .

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To draw a well-labelled diagram to show that p∘q|D*≠q|D*∘p.

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To draw a well-labelled diagram to show that p∘q|D≠q|D∘p.