Question

The average production of peanuts in Virginia is 3000 pounds per acre. A new plant food has been developed and is tested on 59 individual plots of land. The mean yield with the new plant food is 3093 pounds of peanuts per acre, and the population standard deviation is 578 pounds. At a = 0.01, can you conclude that the average production has increased? I don't understand how to work this problem.

Answer 1

Null hypothesis

                   
                      
Alternative hypothesis      

               
                      
We have given,                      
Population mean for given example =3000              
Sample mean=3093              
Population standard deviation =   578              
Sample size for given example =   59              
Level of significance =   0.01              
Z test statistic formula


=1.24

P value is 0.1075............................by using Excel command 1-NORMSDIST(1.24) or by using Z table.

P value is 0.1075 > 0.01

Therefore, we fail to reject H0 at

Conclusion: We do not have sufficient evidence at to say that, the average production has increased.