Construct a 98% confidence interval for the true proportion of adults that are worried about being "hired by a robot." (Round your answer to three decimal places.)

Question

Will there be a time when hiring decisions will be done using a computer algorithm, and without any human involvement? A survey found that 60% of the adults surveyed were worried about the development of algorithms that can evaluate and hire job candidates. To check this claim, a random sample of n = 100

 U.S. adults was selected, with 57 saying they were worried about this issue.

Answer 1

Given we are testing for a true proportion given a sample proportion of a sample size of n>30, we would need to do a one-proportion z-interval (assuming conditions are met):

CI = p̂ ± z√(p̂(1-p̂)/n) where p̂ =57/100=0.57, n=100, and z=2.326 because of the 98% confidence level:

CI = 0.57 ± 2.326√(0.57(1-0.57)/100) ≈ {0.455,0.685}

Hence, we are 98% confident that the true proportion of adults that are worried about being "hired by a robot" is contained within the interval {0.455,0.685}

Hope this helped!