For this discussion post, we are going to construct a confidence interval based on a collection of sample data. Read the following:

We are interested in the average wait estimated time of our local ER at 7 PM on Friday nights. So, we sample 18 estimated wait times (in minutes) at 7 PM on Friday nights over the last 2 years and found the following:

3, 8, 25, 47, 61, 25, 10, 32, 31, 20, 10, 15, 7, 62, 48, 51, 17, 30

Using these ER wait times, construct a 90% confidence interval for the mean ER wait times for Friday nights at 7 PM

1. What is the sample mean and sample standard deviation of this data set?
2. Should we be using the Z or T distribution? Explain why
3. Find the Critical Z or T value for this problem.
4. Compute the Margin of Error, E
5. Write out the confidence interval
6. The ER claims its average wait time on Friday nights will be less than 35 minutes. Based on our confidence interval, does this seem like a valid claim?