How do I go about this?

Question

An entomologist is interested in evaluating a new chemical formulation for possible use as a pesticide for controlling fire ants. She decides to compare its performance relative to the most widely used pesticide on the market, AntKiller. Each of the pesticides is applied to 100 containers of fire ants. The new pesticide successfully killed all the fire ants within two hours of application in 65 of the 100 containers. Of the 100 containers treated with AntKiller only 59 had all fire ants killed. a) Is there significant evidence that the proportion of containers successfully treated by the new formulation is greater than the proportion of containers successfully treated by AntKiller? Test at alpha=0.05 and use the P-value approach.

Answer 1

Let $A$ represent the new pesticide and $B$ be the AntKiller. Then, you are given that $\bar{x}_A = \frac{65}{100} = 0.65$ and $\bar{x}_B = \frac{59}{100} = 0.59$. You know need to find sample variance for both, $$s_A^2 = \sum_n (x_i - \bar{x}_A)^2 = 65(1-0.65)^2 + 35(0-0.65)^2 = 22.75$$ $$s_B^2 = \sum_n(x_i-\bar{x}_B)^2 = 59(1-0.59)^2 + 41(0-0.59)^2 = 24.19$$ You can know do a test for significance $$t = \frac{(\bar{x}_A - \bar{x}_B)}{\sqrt{\frac{s_A}{n_A}+\frac{s_B}{n_B}}}$$ and derive the conclusion from there.