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A group of doctors conducted an experiment to determine which drug is more effective in the treatment of hypertension. Two drugs were tested across three hospitals on 50 patients each. The following table shows the number of patients that reported improvement in hypertension symptoms in each hospital.

\begin{tabular}{|c|c|c|}
\hline
Hospital & Treatment X & Treatment Y \\
\hline
A & 29 & 30 \\
\hline
B & 35 & 21 \\
\hline
C & 26 & 18 \\
\hline
\end{tabular}

Select all true statements that can be concluded from the experiment.

A. Treatment Y's claim to improve the symptoms of hypertension is true.
B. Treatment X's claim to improve the symptoms of hypertension is true.
C. There is not enough information to make any conclusions about the experiment.
D. The percentage of patients showing improvement is higher in Treatment Y.
E. Treatment Y is more effective than Treatment X because there is a greater percentage of patients that showed an improvement.
F. Treatment X is more effective than Treatment Y because there is a greater percentage of patients that showed an improvement.



Answer :

GinnyAnswer
To determine the effectiveness of two treatments tested across three hospitals, we need to analyze the data provided. The number of patients reporting improvement in hypertension symptoms for each treatment in each hospital is given as follows:

[tex]\[ \begin{tabular}{|c|c|c|} \hline Hospital & treatment X & treatment Y \\ \hline A & 29 & 30 \\ \hline B & 35 & 21 \\ \hline C & 26 & 18 \\ \hline \end{tabular} \][/tex]

Each hospital tested the treatments on 50 patients each. We will calculate the percentage of patients showing improvement for each treatment in each hospital.

1. Calculate the percentage of improvements for treatment X in each hospital:

- Hospital A: [tex]\( \frac{29}{50} \times 100 = 58\% \)[/tex]
- Hospital B: [tex]\( \frac{35}{50} \times 100 = 70\% \)[/tex]
- Hospital C: [tex]\( \frac{26}{50} \times 100 = 52\% \)[/tex]

So, the percentages for treatment X are [tex]\( [58\%, 70\%, 52\%] \)[/tex].

2. Calculate the percentage of improvements for treatment Y in each hospital:

- Hospital A: [tex]\( \frac{30}{50} \times 100 = 60\% \)[/tex]
- Hospital B: [tex]\( \frac{21}{50} \times 100 = 42\% \)[/tex]
- Hospital C: [tex]\( \frac{18}{50} \times 100 = 36\% \)[/tex]

So, the percentages for treatment Y are [tex]\( [60\%, 42\%, 36\%] \)[/tex].

3. Calculate the average percentage of improvements for each treatment:

- Average improvement for treatment X:
[tex]\[ \frac{58 + 70 + 52}{3} \approx 60\% \][/tex]

- Average improvement for treatment Y:
[tex]\[ \frac{60 + 42 + 36}{3} \approx 46\% \][/tex]

From these calculations, we can make the following conclusions:

- Treatment X shows an average improvement of approximately 60%.
- Treatment Y shows an average improvement of approximately 46%.

Given that the average improvement percentage for treatment X is higher than treatment Y, we can infer that treatment X is more effective than treatment Y.

Based on the results, the true statements that can be concluded from the experiment are:

B. Treatment X's claim to improve the symptoms of hypertension is true.

F. Treatment X is more effective than treatment Y because there is a greater percentage of patients that showed an improvement.

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