Math  /  Data & Statistics

QuestionQuestion 3, 8.4.63 HW Score: 20\%, 2 of 10 points Part 1 of 6 Points: 0 of 1 Save mework
A study for the treatment of patients with HIV-1 was a randomized, controlled, double-blind study that compared the effectiveness of ritonavir-boosted darunavir (rb the drug currently used to treat HIV-1, with dorovirine, a newly developed drug. Of the 376 subjects taking ritonavir-boosted darunavir, 305 achieved a positive resu Of the 376 subjects taking dorovirine, 326 achieved a positive result. Complete parts (a) and (b). a. Find the sample percentage of subjects who achieved a positive outcome in each group.
The sample percentage of subjects who achieve a positive outcome with ritonavir-boosted darunavir is \square %\%. The sample percentage of subjects who achieve a positive outcome with dorovirine is \square \%. (Round to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We need to calculate the percentage of patients who had a positive outcome in each of the two treatment groups. Watch out! Don't mix up the groups!
Keep the darunavir and dorovirine results separate.

STEP 2

1. Calculate percentage for darunavir.
2. Calculate percentage for dorovirine.

STEP 3

We're given that **305** out of **376** subjects taking ritonavir-boosted darunavir achieved a positive result.
To find the percentage, we'll divide the number of positive outcomes by the total number of subjects in this group and then multiply by 100%.
It's like finding what portion of the pie was eaten, but instead of fractions, we're using percentages!

STEP 4

Let's do the math! 305376100% \frac{305}{376} \cdot 100\%

STEP 5

Calculating the fraction: 3053760.81117 \frac{305}{376} \approx 0.81117

STEP 6

Multiplying by 100% to get the percentage: 0.81117100%=81.117% 0.81117 \cdot 100\% = 81.117\%

STEP 7

Rounding to two decimal places, we get **81.12%**.
So, about **81.12%** of the subjects taking ritonavir-boosted darunavir had a positive outcome.

STEP 8

We know that **326** out of **376** subjects taking dorovirine achieved a positive result.
Just like before, we'll divide the number of positive outcomes by the total number of subjects and multiply by 100% to get the percentage.

STEP 9

Here's the calculation: 326376100% \frac{326}{376} \cdot 100\%

STEP 10

Calculating the fraction: 3263760.86702 \frac{326}{376} \approx 0.86702

STEP 11

Multiplying by 100%: 0.86702100%=86.702% 0.86702 \cdot 100\% = 86.702\%

STEP 12

Rounding to two decimal places gives us **86.70%**.
So, approximately **86.70%** of the subjects taking dorovirine had a positive outcome.

STEP 13

The sample percentage of subjects who achieved a positive outcome with ritonavir-boosted darunavir is 81.1281.12\%.
The sample percentage of subjects who achieved a positive outcome with dorovirine is 86.7086.70\%.

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