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The new management at a bakery claims that workers are now more productive than they were under old management, which is why wages have “generally increased." Let W be Worker i's wage under the old management and let W be Worker i's wage after the change. The difference is D, = W – W. Assume that the D, are a random sample from a Normal (µ, o²) distribution. |(i) Using the following data on 15 workers, construct an exact 95% confidence interval for u. (ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D,) under H,? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of µ = E(D,)? |(iii) Test the null hypothesis from part (ii) against the stated alternative at the 5% and 1% levels. |(iv) Obtain the p-value for the test in part (iii). Worker Wage Before Wage After 8.30 9.25 9.40 9.00 3 9.00 9.25 10.50 10.00 5 11.40 12.00 8.75 9.50 10.00 10.25 9.50 9.50 10.80 11.50 10 12.55 13.10 11 12.00 11.50 12 8.65 9.00 13 7.75 7.75 14 11.25 11.50 15 12.65 13.00

The new management at a bakery claims that workers are now more productive than they were under old management, which is why wages have “generally increased." Let W be Worker i's wage under the old management and let W be Worker i's wage after the change. The difference is D, = W – W. Assume that the D, are a random sample from a Normal (µ, o²) distribution. |(i) Using the following data on 15 workers, construct an exact 95% confidence interval for u. (ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D,) under H,? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of µ = E(D,)? |(iii) Test the null hypothesis from part (ii) against the stated alternative at the 5% and 1% levels. |(iv) Obtain the p-value for the test in part (iii). Worker Wage Before Wage After 8.30 9.25 9.40 9.00 3 9.00 9.25 10.50 10.00 5 11.40 12.00 8.75 9.50 10.00 10.25 9.50 9.50 10.80 11.50 10 12.55 13.10 11 12.00 11.50 12 8.65 9.00 13 7.75 7.75 14 11.25 11.50 15 12.65 13.00

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The new management at a bakery claims that workers are now more productive than they were under old management, which is why wages have “generally increased." Let W be Worker i's wage under the old management and let W be Worker i's wage after the change. The difference is D, = W – W. Assume that the D, are a random sample from a Normal (µ, o²) distribution. |(i) Using the following data on 15 workers, construct an exact 95% confidence interval for u. (ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D,) under H,? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of µ = E(D,)? |(iii) Test the null hypothesis from part (ii) against the stated alternative at the 5% and 1% levels. |(iv) Obtain the p-value for the test in part (iii).
Transcribed Image Text:The new management at a bakery claims that workers are now more productive than they were under old management, which is why wages have “generally increased." Let W be Worker i's wage under the old management and let W be Worker i's wage after the change. The difference is D, = W – W. Assume that the D, are a random sample from a Normal (µ, o²) distribution. |(i) Using the following data on 15 workers, construct an exact 95% confidence interval for u. (ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D,) under H,? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of µ = E(D,)? |(iii) Test the null hypothesis from part (ii) against the stated alternative at the 5% and 1% levels. |(iv) Obtain the p-value for the test in part (iii).
Worker Wage Before Wage After 8.30 9.25 9.40 9.00 3 9.00 9.25 10.50 10.00 5 11.40 12.00 8.75 9.50 10.00 10.25 9.50 9.50 10.80 11.50 10 12.55 13.10 11 12.00 11.50 12 8.65 9.00 13 7.75 7.75 14 11.25 11.50 15 12.65 13.00
Transcribed Image Text:Worker Wage Before Wage After 8.30 9.25 9.40 9.00 3 9.00 9.25 10.50 10.00 5 11.40 12.00 8.75 9.50 10.00 10.25 9.50 9.50 10.80 11.50 10 12.55 13.10 11 12.00 11.50 12 8.65 9.00 13 7.75 7.75 14 11.25 11.50 15 12.65 13.00
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