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.

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 91% 85.9%
large stones 74.3% 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 (square%). (round to one decimal place as needed.)

Explanation:

Step1: Calculate total successful treatments for Treatment 1

For Treatment 1, the number of successful treatments for small stones is 71 and for large stones is 185. So the total successful treatments are $71 + 185=256$.

Step2: Calculate total treatment - group size for Treatment 1

The treatment - group size for small stones is 78 and for large stones is 249. So the total treatment - group size is $78 + 249 = 327$.

Step3: Calculate success rate for Treatment 1

The success rate formula is $\text{Success Rate}=\frac{\text{Number of Successful Treatments}}{\text{Total Treatment - Group Size}}\times100\%$. So the success rate for Treatment 1 is $\frac{256}{327}\times 100\%\approx78.3\%$.

Answer:

78.3