A traffic warden notes the time cars have been illegally parked after their metered time has expired. For 16 offending cars he records the time in minutes as:

10 42 29 11 63 145 11 8 23 17 5 20 15 36 32 15

Obtain an appropriate 95 per cent confidence interval for the median overstay time of offenders prior to detection. What assumptions were you making to justify using the method you did? To what population do you think the confidence interval you obtained might apply?

10 42 29 11 63 145 11 8 23 17 5 20 15 36 32 15

Obtain an appropriate 95 per cent confidence interval for the median overstay time of offenders prior to detection. What assumptions were you making to justify using the method you did? To what population do you think the confidence interval you obtained might apply?

I've been trying to figure out what he means by this. If I'm given a hypothetical median value, like 40, then I can use Wilcoxon or Sign Test to see if the null hypothesis is accepted or rejected. Then I can construct a confidence interval. But he doesn't give any such value. So how can I construct a confidence interval? Do I just use the sample median? If so, then the null will obviously be accepted right? And so I just construct a confidence interval for that?

Does this sound right or am I totally misinterpreting the question?