In a survey of 3371 adults aged 57 through 85​ years, it was found that 81.3​% of them used at least one prescription medication.

Question

Construct a​ 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.

Answer 1

Hi Trinity,

In researching your question, I found multiple similarities throughout the internet, suggesting to me that your question comes from a statistical online learning software system used in your course. Furthermore, this question can be adjusted in terms of numerical values (as seen on the internet) suggesting that the question is evaluating your ability to generate a confidence interval estimate range rather than actual computational skill.

Lastly, your question should contain additional material for it results in a multiple choice response, suggesting either an assignment/quiz/test related question.

With that said, to derive a 90% confidence level interval apply the following steps: (This is akin to finding the middle 90% of data situated between the mean on bell curve)

(1) Find alpha (α) = 10% or 0.10

(2) Find (α/2) = 5% or 0.05

(3) Subtract 0.05 from 1.0000 to get 0.9500

So the interval of a 90% confidence interval is from 0.0500 < p < 0.9500

Find z_α/2 at 0.9500 from z-score normal distribution table yielding z = 1.65

Using z-values → -1.65 < z < 1.65

***Note*** We cannot find the interval range of μ, because the μ is unknown and we need more information, say a standard deviation value to use algebra to work backwards to get the actual mean of the data distribution, but the problem does not provide us this information, suggesting that this problem wants you to find either the p or z range of intervals within 90% confidence.