Question

Two plots at Rothamsted Experimental Station were studied for the production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

6.33	6.05	7.17	5.98	7.31	7.18
7.06	5.79	6.24	5.91	6.14

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.342.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

6.12

7.17

7.73

6.68

7.22

5.58

5.47

5.86

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.710.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of significance.

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

c) What are the degrees of freedom?

dfN=
dfD=

Answer 1

(a)

Using calculator, we found that the sample variance of first and second plots are 0.342 and 0.710 respectively.

H0:

H1:

where are the population variance of wheat straw production in first and second plot respectively.

We will conduct F test to test for the differences in the population variance.

(b)

Test statistic, F =   = 0.710 / 0.342 = 2.076

(Take the largest variance, and divide it by the smallest variance to get the f-value.)

(c)

dfN = n2 - 1 = 8 - 1 = 7

dfD = n1 - 1 = 11 - 1 = 10

Critical value of F at degree of freedom = 7, 10 and = 0.05 is, 3.14

Since the observed F test statistic is less than the critical value, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that population variance of wheat straw production for these two plots are different.