The average production of peanuts in a certain state is 2805 poundsper acre. A n
ID: 2913429 • Letter: T
Question
The average production of peanuts in a certain state is 2805 poundsper acre. A new plant food has been developed and is tested on 56individual plots of land. The mean yield with the new plant food is2980 pounds of peanuts per acre with a standard deviation of 569pounds. At = 0.05, can one conclude that the averageproduction has increased, find the critical value.The critical value is ___.
Explanation / Answer
The averageproduction of peanuts in a certain state is 2805 pounds per acre. Anew plant food has been developed and is tested on 56 individualplots of land. The mean yield with the new plant food is 2980pounds of peanuts per acre with a standard deviation of 569 pounds.At = 0.05, can one conclude that the average production hasincreased, find the critical value. The critical value is = 3471 {Since sample mean yield of 2980 does NOT exceed above Critical Value, we can NOT conclude production increased with the new plant food.} EXPLANATION: {Null Hypothesis} = {H0: = 2805} {Alt Hypothesis} = {H1: >2805} {PopulationMean} = 2805 {Sample Size} = N = 56 {Sample Mean} = (X_bar) = 2980 {Sample Std Dev} = s = 569 {Std Error Of Mean} = s/Sqrt[ N ] = (2980)/Sqrt[ 56 ] = 398.22 {"t" Value For = 0.05, 1-Tail, df=55} = 1.673 {Critical Value} = (2805) + (1.673)*(398.22) = 3471 .
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