Question

the table shows the results when two different techniques are used to treat large and small kidney stones. each entry in the table gives the number of successful treatments and the total size of the treatment group. complete parts a through e.
treatment 1 treatment 2
small stones 76/82 225/258
large stones 181/247 52/78
a. calculate the success rates, expressed as a percentage, of each treatment in both cases. (round to one decimal place as needed.)
treatment 1 treatment 2
small stones 92.7 % 87.2 %
large stones 73.3 % 66.7 %
b. which treatment has the higher success rate for small stones? for large stones?
treatment 1 has the higher success rate for small stones.
treatment 1 has the higher success rate for large stones.
c. now compute the success rate for both treatments when the cases of small and large stones are combined.
treatment 1 has a success rate of %. (round to one decimal place as needed.)

Explanation:

Step1: Calculate total successful treatments for Treatment 1

For Treatment 1, the number of successful small - stone treatments is 76 and large - stone treatments is 181. So the total successful treatments is $76 + 181=257$.

Step2: Calculate total number of treatments for Treatment 1

The number of small - stone treatments for Treatment 1 is 82 and large - stone treatments is 247. So the total number of treatments is $82 + 247 = 329$.

Step3: Calculate success rate for Treatment 1

The success rate formula is $\text{Success Rate}=\frac{\text{Number of Successful Treatments}}{\text{Total Number of Treatments}}\times100\%$. So the success rate for Treatment 1 is $\frac{257}{329}\times100\%\approx78.1\%$.

Answer:

$78.1$