6.79 Corn yield.
The 10-year historical average yield of corn in the United States is about 160 bushels per acre. A survey of 50 farmers this year gives a sample mean yield of bushels per acre. We want to know whether this is good evidence that the national mean this year is not 160 bushels per acre. Assume that the farmers surveyed are an SRS from the population of all commercial corn growers and that the standard deviation of the yield in this population is bushels per acre. Report the value of the test statistic , give a sketch illustrating the -value and report the -value for the test of
Are you convinced that the population mean is not 160 bushels per acre? Is your conclusion correct if the distribution of corn yields is somewhat non-Normal? Why?
6.79
. -value = 0.0238. There is evidence that the population mean is not 160 bushels per acre. Yes, the conclusion is still correct for non-Normality because of the central limit theorem.