When the NDP formed the provincial government in 1999, the mean wait time for a particular type of surgery was 60 days. Public health officials take a sample of 30 individuals who have had the surgery in 2011 and record the number of days the patients had to wait prior to having surgery. The data are as follows:
9 14 18 23 26 31 37 40 41 41 43 52 54 57 58
61 65 65 67 69 69 72 74 76 76 77 80 81 87 89
The population standard deviation of wait time for this type of surgery is known to be 20 days.
(a) Using JMP, create a histogram for this data set. What is the shape of the distribution of wait times?
(b) It is clear from the histogram in (a) that wait times do not follow a normal distribution. Why is it nevertheless appropriate to use inference methods which rely on the assumption of normality?
(c) Using JMP, conduct an appropriate hypothesis test at the 1% level of significance to determine whether the true mean wait time has decreased since the NDP formed government. (You will have to write out the hypothesis and the conclusion - JMP will give you the test statistic and the P-value.)
(d) Provide a carefully worded interpretation of the P-value calculated in part (a) which can be understood by someone with little or no knowledge of statistics.
(e) Use JMP to find the 95% confidence interval for the true mean wait time for surgery.