Question

Management is interested in developing a regression model to predict the average amount of time it takes to process a given number of invoices. That is, the num- ber of invoices is the explanatory variable, and processing time is the response. Over a 30-day period, data are collected on the number of invoices processed and the total time taken, in hours. (a) The manager is interested in making an inference about the start-up time, that is, the processing time before the workers begin to process the invoices (due to collecting the invoices, logging in to the computer, etc.). What sort of inference would you make to answer this question? (l.e. A confidence interval, prediction interval, or p-value? Which one?) (b) The manager believes a best practice benchmark for the average processing time for one additional invoice is 0.01 hours. What sort of inference would you make to answer whether that benchmark is appropriate for these workers? (c) Frequently, the company has around 130 invoices to process by the end of the day. The manager wants to identify problems when processing time is very low (and incidentally, very high, as employees may be taking shortcuts). What sort of inference should be made to identify how long the processing time is in 95% of cases where there are 130 invoices to process?

Answer 1

(a). The prediction interval would be appropriate to answer this question, since, the manager wants to know the processing time before the workers begin to process invoice, that is, the manager wants to predict the processing time before the workers begin to process invoice.

(b). The estimation of p-value would be appropriate in order to answer whether the benchmark for average processing time is 0.01.

(c). The confidence interval would be the appropriate inference, in order to identify how long the processing time is in 95% of the cases when there are 130 invoices to process.