Question

A Drug testing as precondition for employment has a long history in the United States. It was started during the 1980s "War on Drugs." The state of colorado legalized marijuana possession, sale and distribution in 2014. That has influenced the willingness of Colorado Companies to test employees for drug use as part of the hiring process. A recent RANDOM SURVEY of 609 employers found that 402 were still testing for drug use.

a) What is the 99% confidence Interval for the proportion of companies that test for drug use in colorado?

b) The American Management Association recently stated that the proportion of US companies involved with pre-employment drug testing is .62. Please formulate the null and alternative hypothesis for the question of whether the random sample evidence from colorado is consistent with this fact about the United States as a whole. [we need only the elements involved in STEP 1 of hypothesis testing]

c) A second Issue is the tradeoffs in testing. Most testing companies test for heroin, cocaine, marijuana, methamphetamines, and opioids (the Street Drugs) they do not test for other forms od rugs being used.

part 1 of part c) if the null hypothesis is that the worker is drug free, how would you define the type 1 and type 2 error associated with administering a drug test to a potential employee ( in words). What are some of the tradeoffs for each type of error?

part 2 of part c) in 2009, the unemployment rate was about 9 percent. in 2018 the unemployment rate is about 4 percent. Would this change in the labor market influence the acceptable level of type1 or type 2 erros? how? please briefly explain your thinking.

Answer 1

a)

Sample    X    N Sample p         99% CI
1          402 609 0.660099   (0.610657, 0.709540)

b)

c)

type i error - rejecting the null when it is false
hence concluding that the worker is using drug when infact they are drug free

type ii error - fail to reject the null when it is true
hence fail to conlude that they are using drugs when
in fact they are using drugs