Answer Happy

There have been a record number of firsts in this year's A-level exams in Britain. As a result, student applications at Royal Excellence University are flooding in. The university's chancel- lor wants to avoid any delays in processing these applications and communicates a target of processing at least 1000 applications per week. He gets sample data from 20 departments and finds that the average number of processed applications in each department is 995 with a sample variance of 250. In a press conference the next day the chancellor claims that the target of at least an average 1000 processed applications per week and department is still being met. Does the provided evidence support the chancellor's claim at a 5% significance level? Show your workings.