Suppose that you want to estimate the mean time it takes driversto react following the application of brakes by the driver in frontof them. You take a sample of reaction time measurements andcompute their mean to be 2.5 seconds and their standard deviationto be 0.4 seconds. For each of the following sampling scenarios,determine which test statistic is appropriate to use when makinginference statements about the population mean.
| Sampling Scenario | Z | t | could use either Z or t | unclear |
| (1) The sample has size 11, and it is from a population with adistribution about which we know very little. | | | | |
| (2) The sample has size 85, and it is from a non-normallydistributed population. | | | | |
| (3) The sample has size 16, and it is from a normally distributedpopulation with a known standard deviation of 0.45. | | | | |
| (4) The sample has size 20, and it is from a normally distributedpopulation with unknown standard deviation. | | | | |
| (5) The sample has size 75, and it is from a non-normallydistributed population with a known standard deviation of0.45. | | | | |
