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Medicine A treats Symptom Y. 400 subjects with Symptom Y volunteered to take Medicine A, and 160 were treated effectively.

In order to estimate the medicine's efficacy with 95% confidence, which statistical method should be used?

A. TInterval
B. 2-SampTInt
C. 2-PropZInt
D. 2-SampZInt
E. ZInterval
F. 1-PropZInt

Answer :

To estimate the efficacy of Medicine A with 95% confidence, we need to analyze the proportion of subjects who were treated effectively. In this scenario, we're dealing with a single proportion (those treated effectively out of all participants), so the appropriate statistical method to use is the 1-PropZInt.

Here's how you can determine the correct method step-by-step:

  1. Identify the Scenario: You have a single group of subjects (400 total) and you're observing the outcome (160 treated effectively). This is a classic single-proportion situation, where you want to estimate the proportion of success.

  2. Formulate the Problem: You want to calculate the confidence interval for the proportion of subjects effectively treated by Medicine A, based on a sample.

  3. Choose the Correct Method: For a single proportion confidence interval, you use 1-PropZInt (1-Proportion Z-Interval). This method calculates the range of percentages in which the true proportion is expected to fall, with a certain level of confidence (95% in this case).

  4. Calculate the Interval:

    • Let [tex]p[/tex] be the sample proportion, calculated as [tex]\frac{160}{400} = 0.4[/tex].
    • The formula for a 1-PropZInt is given by the expression:
      [tex]\hat{p} \pm Z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}[/tex]
      where [tex]\hat{p}[/tex] is the sample proportion, [tex]n[/tex] is the sample size, and [tex]Z[/tex] is the Z-score corresponding to the desired confidence level (1.96 for 95% confidence).

  5. Interpret the Results: After performing the computation, you'll get a confidence interval which tells you the range in which the true effectiveness of the medicine likely falls. This provides a statistical backing to the claim of the medicine's efficacy.

Thus, for estimating the efficacy of Medicine A using the results from this study, you should use the 1-PropZInt.

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