Question

An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 17 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 17 differences (Variety A - Variety B) give x¯=3.98 and s=3.64. Does this sample provide evidence that Variety A had a higher yield than Variety B?

(a) State the null and alternative hypotheses: (Type "mu" for the symbol μ , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)

H0 :

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)

Answer 1

Given difference of mean S= 3.64

H0 : μ ( difference of population mean A&B)=0

Ha : μ >0 that is Variety A had a higher yield than Variety B.

(b) The test statistic,

  

  

The test statistic t = 4.508

p value = 0.000179

Conclusion:   p value 0.000179 <0.05 Reject H0

This sample provide evidence that Variety A had a higher yield than Variety B at 5% level of significance  

Yes