Investigation to review key ideas and then we

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investigation to review key ideas and then we parallel Chapter 3 in first considering random sampling and then random assignment, both for scope of conclusions but also for how we will design our simulation. Investigation 4.1: Employment Discrimination? Robert Martin turned 55 in 1991. Earlier in that same year, the Westvaco Corporation, which makes paper products, decided to downsize. They ended up laying off roughly half of the 50 employees in the engineering department where Martin worked, including Martin. Later that year, Martin went to court, claiming that he had been fired because of his age. A major piece of evidence in Martin’s case was based on a statistical analysis of the relationship between the ages of the workers and whether they lost their jobs. Part of the data analysis presented at his trial concerned the ten hourly workers who were at risk of layoff in the second of five rounds of reductions. At the beginning of Round 2 of the layoffs, there were ten employees in this group. Their ages were 25, 33, 35, 38, 48, 53, 55, 55, 56, 64. Three were chosen for layoff: the two 55-year-olds (including Martin) and the 64-year old. (a) Create stacked dotplots of the ages of the employees who were retained and laid off. retained laid off Do these data seem to support the claim that the laid-off employees tended to be older than those who were not laid off? (b) One way to measure this support is to compare the difference in the average ages of the two groups. Calculate the mean age of the employees that were laid off and the mean age of the employees that were not laid off ( ) retained off laid x x ± ± . (c) Although we see some evidence of an age difference, on average, between these two groups, it’s still possible that the employers just randomly decided which three employees to layoff. How would you expect the behavior of these dotplots to compare if the layoff decisions had been made completely at random?
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Chance/Rossman, 2015 ISCAM III Investigation 4.1 256 (d) Describe how you could generate one “could have been” observation under this assumption that the lay-off decisions are made completely at random. (e) If we consider the outcomes where three of the ten employees are laid off, how many of these outcomes are “as extreme” as the observed result? How many are “more extreme”? [ Hint : List the ages of the three employees that are laid off for these results.] (f) How many different ways are there to form these two groups, three to be laid off and seven retained, if the decisions are made completely at random? (g) How many of these random splits have three of the four oldest people in the laid-off group? The dotplot below shows all possible values for the “difference in mean age” for the laid -off group minus the retained group for all possible splits into 3 laid-off employees and 7 retained.
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