For the lettuce yield data, (page 494) it is thought that

Chapter 6, Problem 5E

(choose chapter or problem)

For the lettuce yield data (page 499), it is thought that the yields from fertilizer A might have a larger variance than the yields from fertilizer B.

a. Compute the sample variances \(s_{A}^{2}\) and \(s_{B}^{2}\) of the yields assigned to A and B, respectively, and the quotient \(s_{A}^{2} / s_{B}^{2}\).

b. Someone suggests using the F test in Section 6.11 for this problem. Is this a good idea? Why or why not?

c. Perform a randomization test of \(H_{0}: s_{A}^{2} \leq s_{B}^{2}\) versus \(H_{1}: s_{A}^{2}>s_{B}^{2}\), using the test statistic \(s_{A}^{2} / s_{B}^{2}\),  and a minimum of 1000 random outcomes. (Hint: Proceed just as in the example in the text, but for each outcome compute \(s_{A}^{2}\), \(s_{B}^{2}\), and \(s_{A}^{2} / s_{B}^{2}\) rather than \(\overline{A}\), \(\overline{B}\), and \(\overline{B}-\overline{A}\), A fair amount of coding may be required, depending on the software used.)

Equation Transcription:

Text Transcription:

s_A^2

s_B^2

s_A^2/s_B^2

H_0:s_A^2{</=}s_B^2

H_1:s_A^2>s_B^2

s_A^2/s_B^2

s_A^2

s_B^2

s_A^2/s_B^2

overline{A}

overline{B}

overline{B}-overline{A}