Question

Corn yield. The mean yield of corn in the United States is about 135 bushels per acre. A survey of 50 farmers this year gives a sample mean yield of x ̅= 138.4 bushels per acre. We want to know whether this is good evidence that the national mean this year is not 135 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 σ= 10 bushels per acre. Conduct a hypothesis test to determine if the corn yield has changed using 0.05 as significant level. Write out the hypotheses and report the P-value. Are you convinced that the population mean is not 135 bushels per acre?

Answer 1

Solution :

= 135

= 138.4

= 10

n = 50

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 135

Ha : 135

Test statistic = z

= ( - ) / / n

= (138.4 - 135) /10 / 50

= 2.404

p(Z >2.404 ) = 1-P (Z < 2.404) = 0.0081 *2 = 0.0162

P-value = 0.0162

= 0.05  

0.0162< 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that the population mean is not 135 bushels per acre.