A firm assumes that idle time of workers in construction projects is 72 minutes give or take 20 minutes. A random sample of 30 workers yields a mean idle time of 76 minutes on a current project. Test the hypothesis that idle time is greater than 72 minutes at the five percent level of significance on this current project!
a. Draw the power curve and compute the probability of concluding the workers are not up to par for some actual population means in the alternative set.
b. Compute the probability of a type 2 error if the workers are idle 80 minutes out of the day. Based on your calculation what would you recommend?
c. If the mean idle time exceeds 80 minutes, the firm needs to have only a five percent chance of concluding that the workers are doing the job. How large a sample should be selected in order to differentiate between population at 72 and those at 80?