Question

population mean=42.6
standard deviation=12

n=16
M=34.4. Is this mean a reasonable outcome for a sample of n=16, or is this sample mean very different from what would usually be expected?

I obtained a z -score of -2.73. Thus, that would make the sample mean a reasonless outcome. Am I correct?

Answer 1

For a sample of 16, the snadard deviation of the mean should be reduced by a factor of sqrt 16 = 4 to be 12/4 = 3. If the measured mean is 34.4, which is 8.2 below the expected mean, the z-score is -8.2/3 = -2.73.

I don't know what you mean by a "reasonless" outcome. It is not unreasonable, but it is quite unlikely (0.31% probability that the measured mean will be this low or lower).

Answer 2

I meant REASONABLE, sorry. Thanks!