Question

An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 12 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 12 differences (Variety A - Variety B) give x¯=3.24x¯=3.24 and s=5.56s=5.56. 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 μμ , 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)

(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

a)

Ho: mu =0

Ha: mu >0

b)

sample mean 'x̄=	3.240
sample size    n=	12.00
std deviation s=	5.560
std error ='sx=s/√n=	1.6050
test stat t ='(x-μ)*√n/sx=	2.0186

c)

0.05 level with right tail test and n-1= 11 df, critical t=

1.796

since test statistic >critical value

we reject null hypothesis

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