Question

in a study of pain relievers, 50 people were given product a, and all but 12 experienced relief. in the same study, 20 people were given product b, and all but 4 experienced relief. fill in the blanks below to make the most reasonable statement possible. product select performed worse in the study. that is because % failed to get relief with this product, whereas only % failed to get relief with product select.

Explanation:

Step1: Calculate failure - rate for product A

The number of people given product A is $n_A = 50$, and the number of people who did not experience relief is $12$. The failure - rate formula is $\text{Failure - rate}=\frac{\text{Number of non - relieved}}{\text{Total number of people}}\times100\%$. So for product A, the failure - rate $r_A=\frac{12}{50}\times100\% = 24\%$.

Step2: Calculate failure - rate for product B

The number of people given product B is $n_B = 20$, and the number of people who did not experience relief is $4$. Using the failure - rate formula, for product B, the failure - rate $r_B=\frac{4}{20}\times100\%=20\%$.

Step3: Compare the failure - rates

Since $24\%>20\%$, product A has a higher failure - rate.

Answer:

Product A performed worse in the study. That is because 24% failed to get relief with this product, whereas only 20% failed to get relief with Product B.