Question

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).

3.66 3.72 4.29 3.87 4.11 3.79 4.09 4.42 3.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39

Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.313. Another random sample of years for a second plot gave the following annual wheat production (in pounds).

3.58 3.55 3.55 3.58 3.49 3.72 4.13 4.01 3.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35

Use a calculator to verify that the sample variance for this plot is s2 ≈ 0.097. Test the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot. Use a 10% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

dfN
dfD

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Answer 1

The statistical software output for this problem is:

From above output:

a) Level of significance = 0.10

Hypotheses:

Ho:

Ha:

b) Sample F = 3.23

dfN = 15

dfD = 15

c) P - value = 0.0149

d) Reject Ho