Answer to Question #160547 in Statistics and Probability for elyn

Question

Two types of rice varieties are being considered for yield and a comparison is needed. 28 hectares were planted with rice varieties exposed to fairly uniform growing conditions. The results are tabulated below:

Variety A Variety B

Average yield 68 sacks/ha 52 sacks/ha

Sample Variance 7.2 10.4

Is there a significant difference between variety A and variety B @ 5% significant level.

Answer 1

We should use t-test:

1) H₀: $\mu_1=\mu_2$ and H₁: $\mu_1\ne\mu_2$

2) $\alpha=0.05$; two-tailed; d.f. = 28-1 = 27

critical values = 2.052 and -2.052

3) $t=\frac{(\overline{X}_1-\overline{X}_2)-(\mu_1-\mu_2)}{\sqrt{s^2_1/n_1+s^2_2/n_2}}=\frac{68-52}{\sqrt{7.2/28+10.4/28}}=20.18$

4) 20.18>2.052, so we should reject the null hypothesis

5) There is a significant difference between variety A and variety B