Question

Couriers such as UPS and FedEx compete on service and price. One way to reduce costs is to keep labor costs low by hiring and laying off workers to meet demand. This strategy requires managers to hire and train new workers. But newly hired and trained workers are not as productive as more experienced ones. Thus, determining the number of workers required and the work schedule is difficult. The current work schedule is based on the belief that trainees will achieve more than 90% of the level of experienced workers within 1 week of hiring. To determine the accuracy of this number, an operations manager conducted an experiment. The manager hired 50 trainees and observed them for 1 hour and recorded the numbers of packages processed and routed. The sample mean is 460.38 and the sample standard deviation is 38.83. It is known that experienced workers process an average of 500 packages per hour. The manager is concerned that if he concludes that the mean is greater than 450 when it isn’t, the result will be some late deliveries. Find the p-value for this hypothesis test. H_{a} \::\mu>450

Answer 1

Test statistics

t = - ​​​​​​ / S / sqrt(n)

= 460.38 - 450 / 38.83 / sqrt(50)

= 1.89

This is test statistics value.

From T table,

At df = 49 and with test statistics t = 1.89

p-value = 0.0323