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).

4.17	4.17	3.99	3.63	3.69	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 ≈ 0.312.

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

4.09	3.40	3.40	3.82	3.64	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 ≈ 0.105.

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 1% level of significance.

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

Answer 1

Part a)

F3:M4 and F8:M9 is the range of values of first and second plot.

Excel formula

VAR.S(F3:M4) = 0.311993333 ≈ 0.312

VAR.S(F8:M9) = 0.105465 ≈ 0.105

Part b)

To Test :-

H0 :-  

H1 :-  

Test Statistic :-

f = 0.312 / 0.105
f = 2.9714

Test Criteria :-
Reject null hypothesis if f > f(α,n1-1 , n2-1)
f(0.01 , 15 , 15 ) = 3.5222
f < f(0.01,15 , 15 ) = 2.9714 < 3.5222 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot.