An administrator at a medium-sized hospital tells the board of directors that, among patients received at the Emergency room and eventually admitted to a ward, the average length of time between arriving at Emergency and being admitted to the ward is 4 hours and 15 minutes. One of the board members believes this figure is an underestimate and checks the records for a sample of 25 patients. The sample mean is 6 hours and 30 minutes. Assuming that the population standard deviation is 3 hours, and that the length of time spent in Emergency is normally distributed, use the sample data to determine whether there is sufficient evidence at the 5% level of significance to assert that the administrator's claim is an underestimate.
(a) According to the null hypothesis, the value of the population mean isAnswerhours. (Give your answer in hours to 3 decimal places x.xxx(notin hours and minutes))
(b) Is the test one-tailed or two-tailed? Answer:Answer(answer 1 or 2)
(c) To 3 decimal places the critical value of the test statistic for this hypothesis test is:Answer(Answer in the form x.xxx or -x.xxx)
(d) To 3 decimal places the test statistic calculated from the sample is:Answer (Answer in the formx.xxx or -x.xxx)
(e) Is the null hypothesis rejected at the 5% level? Answer:Answer(Answer YES or NO)
(f)Does this mean that the hospital administrator provided accurate information to the board? Answer:Answer(Answer YES or NO)
(g) Is the assumption that the number of beds filled is normally distributed necessary in order to perform this test?? Answer(Answer YES or NO)