Question

an agricultural scientist is comparing maize yields per acre for which a nitrate based fertilizer has been used to those from plots having a Sulphur based fertilizer. A sample of 100 acres using nitrate has yielded an average of 56.2 bags per acre with a standard deviation of 12.5 bags. The sample of 150 acres with sulphur fertilizer has yielded an average of 52.6 bags per acre with a standard

deviation of 13.8 bags. Test the relevant hypothesis to validate or invalidate whether

nitrate based fertilizer is superior at 10 percent significance level

Answer 1

$\mu_1$ is mean nitrate based fertilizer

$\mu_2$ is mean Sulphur based fertilizer

$H_0:\mu_1=\mu_2$ , nitrate based fertilizer is not superior

$H_a:\mu_1<\mu_2$ , nitrate based fertilizer is superior

$t=\frac{\overline{x}_1-\overline{x}_2}{\sqrt{s^2_1/n_1+s^2_2/n_2}}=\frac{56.2-52.6}{\sqrt{12.5^2/100+13.8^2/150}}=2.139$

$df=\frac{(s_1^2/n_1+s^2_2/n_2)^2}{\frac{(s_1^2/n_1)^2}{n_1-1}+\frac{(s^2_2/n_2)^2}{n_2-1}}=226$

critical value:

$t_{crit}=-1.652$

Since $t>t_{crit}$ , we accept the null hypothesis. Nitrate based fertilizer is not superior