90-777/95-796 Assignment 2 Due: By midnight EST Tuesday, September 19 by upload to Gradescope Q.1 The purpose of job training is to improve employability and wages. Sometimes, however, it backfires and actually has the opposite effect if, for example, a trainee is discouraged by the experience. The table below shows the probability of hypothetical wage outcomes for high school graduates with and without job training. Type Unemployed (0 $/hr.) $8/hr. $12/hr. $18/hr. No job training .1 .5 .20 .20 Job Training .15 .35 .15 .35 Q1.1 What is the difference in expected wage across all wage categories between high school graduates who do and do not receive job training? Q1.2 Per the Module 3d lecture, this calculation equals the Population Average Treatment Effect (PATE). Does this calculation of PATE suggest that job training is effective in increasing wages? Q1.3. What is the probability of being employed among those with job training? What is the probability of being employed among those without job training? Do these probabilities suggest job training is effective in increasing the chances of being employed?
Q1.4. What is the expected wage of those who receive job training and are employed? Q1.5. Suppose 30% of high school graduates receive job training. What percentage of high school graduates will be unemployed? Q2The output below pertains to the participants in the Fast Food experiment. It reports summary statistics for the variable “dieting” by the respondent’s self-identified race. Variable “dieting” is coded as 1 if the respondent reported he/she was dieting, and 0 if the respondent reported no. From this table, calculate the probability that a randomly chosen participant in this experiment is dieting. Show the basis for your calculation and perform this calculation with relevant probabilities calculated to the thousandth (e.g, 0.342, 0.096, 0.004). (Note: You’ll observe that the top row constituing 22 respondents reports no race. Do not include this group in your calculation.) Q.3. For budgeting purposes, each manager in a company must estimate their group’s monthly expenses. Manager 1 estimates that her monthly expenses are uniformly distributed between $5,000 and $45,000. Manager 2 estimates that his monthly expenses are normally distributed with mean $21,000 and standard deviation $3,000. Manager 3 estimates that her monthly expenses follow a discrete distribution with p($15, 000) = 0.2, p($20, 000) = 0.4, p($25, 000) = 0.3, and p($30, 000) = 0.1. Q3.1. For each of the three managers, compute the mean and standard deviation of their group’s monthly expenses. (For the uniform distribution use the formula shown in the Module 3e lecture.) Q.3.2. For each of the three managers, estimate the probabilities that their group’s monthly expenses are: i) between $17,000 and $24,000, ii) higher than $22,000, iii) below $18,000, and iv) exactly $25,000.
Q.3.3. The company wants to budget enough for each group so that the probability of expenses being over budget is at most 15%. How much should the company budget for each manager? Q.4. A manufacturer produces 1000 computer chips for a mission-critical application. Each chip costs $100 to manufacture and sells for $3000, but has a 2% chance of being defective. Q4.1. Compute the mean and standard deviation of the number of defective chips. Q.4.2. Assume that 99% of defective chips are discovered (and destroyed) before they are sold, while the other 1% are sold with defects. The manufacturer suffers an estimated loss of $5,000,000 for each defective chip sold (due to lawsuits, penalties, and bad public relations). What is the manufacturer’s expected profit? Q.4.3 The manufacturer develops a new quality control technology which enables detection of 100% of defective chips. How much would the implementation of this technology increase the manufacturer’s expected profit?
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