Math  /  Data & Statistics

Questionall 2024 Nathalie Sanchez Question 3, 8.4.63 HW Score: 21%,2.121 \%, 2.1 of 10 points Homework Part 1 of 6 Points: 0.1 of 1 Save
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 (rbd), the drug currently used to treat HIV-1, with dorovirine, a newly developed drug. Of the 389 subjects taking ritonavir-boosted darunavir, 309 achieved a positive result. Of the 389 subjects taking dorovirine, 319 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 %\%. The sample percentage of subjects who achieve a positive outcome with dorovirine is \%. (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 dorovirine and ritonavir-boosted darunavir results separate.

STEP 2

1. Calculate percentage for ritonavir-boosted darunavir.
2. Calculate percentage for dorovirine.

STEP 3

Alright, let's dive into the ritonavir-boosted darunavir group!
We know that **309** out of **389** subjects had a positive outcome.
To find the percentage, we'll divide the number of positive outcomes by the total number of subjects in this group.
This gives us a proportion representing the positive outcomes within the group.

STEP 4

3093890.7943 \frac{309}{389} \approx 0.7943 So, about **0.7943** of the subjects in the ritonavir-boosted darunavir group had a positive outcome.

STEP 5

To convert this proportion to a percentage, we **multiply by 100**.
This shifts the decimal point two places to the right, giving us a percentage representation. 0.7943100=79.43 0.7943 \cdot 100 = 79.43 So, approximately **79.43%** of the subjects taking ritonavir-boosted darunavir had a positive outcome.

STEP 6

Now, let's move on to the dorovirine group!
We're given that **319** out of **389** subjects had a positive outcome.
Just like before, we'll divide the number of positive outcomes by the total number of subjects to get the proportion of positive outcomes.

STEP 7

3193890.8175 \frac{319}{389} \approx 0.8175 This tells us that roughly **0.8175** of the subjects in the dorovirine group had a positive outcome.

STEP 8

To express this as a percentage, we'll **multiply by 100**, moving the decimal point two places to the right. 0.8175100=81.75 0.8175 \cdot 100 = 81.75 Therefore, about **81.75%** of the subjects taking dorovirine had a positive outcome.

STEP 9

The sample percentage of subjects who achieved a positive outcome with ritonavir-boosted darunavir is \textbf{79.43%}.
The sample percentage of subjects who achieved a positive outcome with dorovirine is \textbf{81.75%}.

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