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 x¯=2.82 and s=6.96. 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)

Step-by-step explanation:

1) H0 : Mean of variety A - Variety B = 0

  Ha : Mean of variety A - Variety B>0

(one tailed test)

(b) Find the test statistic, t = Mean difference / std error

Std error = std dev/sqrt n =

(c) Answer the question:

Does this sample provide evidence that Variety A had a higher yield than Variety B?

df = 14-2 =12

p value = 0.043

Since p<0.05, (our significance level) reject H0.

Yes. this sample provides evidence that Variety A had a higher yield than Variety B

answer for #1 is c

answer for #2 is d

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.