(4 points) An agricultural field trial compares the yield of two varieties of co

Question

(4 points) An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 14 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 14 differences (Variety A- Variety B) give 2.55 and s 5.3. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the nulil and alternative hypotheses: (Type "mu" for the symbol , e.g. mu > 1 for the mean is greater than 1, mu 1 for the mean is less than 1, mu not1 for the mean is not equal to 1) Ho Ha (b) Find the test statistic, t (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than variety B? (Use a 5% level of significance) Type: Yes or No)

Explanation / Answer

(a) Ho: A B and Ha: A > B

(b)

Data:     

n = n1 = n2 14    

d-bar = 2.55    

s (of d) = 5.3    

Hypotheses:     

Ho: d-bar 0    

Ha: d-bar < 0    

Decision Rule:     

= 0.05    

Degrees of freedom = 14 - 1 = 13

Critical t- score = -1.770933383   

Reject Ho if t < -1.770933383    

Test Statistic:     

SE = s/n = 5.3/14 = 1.416484582   

t = d-bar/SE = 2.55/1.41648458213585 = 1.800231384   

p- value = 0.047530397    

(c) Decision (in terms of the hypotheses):    

Since 1.800231384 < -1.771 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

It appears that A > B.   

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