Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 9 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows: 2.5 2.5 2.8 3 2.8 2.4 2.1 2 3 What is a point estimate for the population mean length of time. (Round answer to 4 decimal places) (2 points) Which distribution should you use for this problem? (1 point) O normal distribution Ot-distribution What must be true in order to construct a confidence interval in this situation? (1 point) O The population mean must be known O The population standard deviation must be known O The sample size must be greater than 30 O The population must be approximately normal Construct a 99% confidence interval for the population mean length of time. Enter your answer as an open- interval (i.e., parentheses) Round upper and lower bounds to two decimal places (4 points) What does it mean to be "99% confident" in this problem? (2 points) 99% of all simple random samples of size 9 from this population will result in confidence intervals that contain the population mean O The confidence interval contains 99% of all samples O There is a 99% chance that the confidence interval contains the population mean Suppose that the company releases a statement that the mean time for all patients is 2 hours. Is this possible? (1 point)