Your firm manufactures medicine which is dispensed into bottles. The mean fill level for the medicine bottles is supposed to be 200 ml. You take a random sample of 13 bottles and find the following fill levels (in milliliters):
195, 195, 200, 198, 204, 195, 201, 199, 204, 195, 196, 202, 199
Assume that the fill levels are Normally distributed in the entire population. Assume that the population standard deviation for all fill levels of medicine bottles σ is unknown.
Construct and interpret 90% confidence interval for the mean fill level μ of medicine bottle. Write a statement which correctly states the meaning of this interval in the context of the problem.
Round all final answers to 2 decimal places, if needed.
(a) The average fill level for the sample of 13 medicine bottles is
(b) We are 90% confident that the mean fill level of medicine bottles μ is between and (milliliters)