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The medication usage of adults aged 57 through 85 years is recorded. In a sample of 3005 adults aged 57 through 85 years, 81.7% of them use at least one prescription medication.

a.

The number of adults aged 57 through 85 years who use at least one prescription medication is equal to:

\(\begin{array}{c}81.7\% \;{\rm{of}}\;3005 = \frac{{81.7}}{{100}} \times 3005\\ = 2455\end{array}\)

Therefore, the number of adults aged 57 through 85 years who use at least one prescription medication is equal to 2455.

The confidence interval has the following expression:

\(\hat p - E < p < \hat p + E\)

Here, E is the margin of error and has the following formula:

\(E = {z_{\frac{\alpha }{2}}} \times \sqrt {\frac{{\hat p\hat q}}{n}} \)where

\(\hat p\)is the sample proportion of adults aged 57 through 85 years who use at least one prescription medication.

\(\hat q\)is the sample proportion of adults aged 57 through 85 years who do not use any prescription medication.

n is the sample size

\({z_{\frac{\alpha }{2}}}\) is the one-tailed critical value of z

The confidence level is given to be equal to 90%. Thus, the corresponding level of significance is equal to 0.10.

Now, \(\alpha = 0.10\)

The value of \({z_{\frac{\alpha }{2}}}\) form the standard normal table is equal to 1.645.

The margin of error is computed as shown below:

\(\begin{array}{c}E = {z_{\frac{\alpha }{2}}} \times \sqrt {\frac{{\hat p\hat q}}{n}} \\ = 1.645 \times \sqrt {\frac{{0.817 \times 0.183}}{{3005}}} \\ = 0.0116\end{array}\)

b.

The value of the confidence interval is computed as follows:

\(\begin{array}{c}\hat p - E < p < \hat p + E\\0.817 - 0.0116 < E < 0.817 + 0.0116\\0.8054 < p < 0.8286\\80.54\% < p < 82.86\% \end{array}\)

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is equal to (80.54%, 82.86%).

c.

The above results do not suggest anything about the proportion of college students who use at least one prescription medication because the sample consisted of only adults aged 57 through 85 years.