Question

Suppose that you want to estimate the mean time it takes drivers to react following the application of brakes by the driver in front of them. You take a sample of reaction time measurements and compute their mean to be 2.5 seconds and their standard deviation to be 0.4 seconds. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference 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 a distribution about which we know very little.
(2) The sample has size 85, and it is from a non-normally distributed population.
(3) The sample has size 16, and it is from a normally distributed population with a known standard deviation of 0.45.
(4) The sample has size 20, and it is from a normally distributed population with unknown standard deviation.
(5) The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 0.45.

Answer 1

If we are given sample size n from normal distribution with sample mean and Population standard deviation in such case we use z test.

If we are given sample size n from normal distribution with sample mean and sample standard deviation in such case we use t test (Population standard deviation unknown)

Sampling Scenario	Z	t	could use either Z or t	unclear
(1) The sample has size 11, and it is from a population with a distribution about which we know very little.		t . Population standar deviation unknown.
(2) The sample has size 85, and it is from a non-normally distributed population.				unclear
(3) The sample has size 16, and it is from a normally distributed population with a known standard deviation of 0.45.	Z. Population satndard deviation 0.45
(4) The sample has size 20, and it is from a normally distributed population with unknown standard deviation.		t . Population standar deviation unknown.
(5) The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 0.45.				unclear

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