https://file.aiquickdraw.com/mathbot/file/1727658555571o1bijsfk.jpg

Let's work through each of the questions based on the information in the image.

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**Question 1: What is the parameter being estimated?**

- **Answer**: The parameter being estimated is the *population mean* number of drugs prescribed per admission. The investigator is trying to estimate the average number of drugs prescribed to all patients in the hospital based on a sample.

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**Question 2: What is the point estimate of this population parameter?**

- **Answer**: The point estimate is the sample mean, which is given as 7.6 drugs per admission. This is the best single estimate of the population mean based on the sample data.

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**Question 3: If the investigator computed a standard deviation of 1.13, construct and interpret a 95% and a 99% confidence interval estimate for the parameter being estimated.**

To compute confidence intervals, we use the formula:

\[
CI = \bar{x} \pm z \times \frac{\sigma}{\sqrt{n}}
\]

Where:
- \( \bar{x} = 7.6 \) (sample mean)
- \( \sigma = 1.13 \) (sample standard deviation)
- \( n = 92 \) (sample size)
- \( z \) is the z-score corresponding to the desired confidence level.

For a 95% confidence level, the z-score is approximately 1.96.  
For a 99% confidence level, the z-score is approximately 2.576.

Let's calculate these confidence intervals.

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### 95% Confidence Interval:

\[
CI_{95\%} = 7.6 \pm 1.96 \times \frac{1.13}{\sqrt{92}}
\]

### 99% Confidence Interval:

\[
CI_{99\%} = 7.6 \pm 2.576 \times \frac{1.13}{\sqrt{92}}
\]

I'll now calculate the values for both intervals.

To improve the health care delivery system in a tertiary hospital, a computerized procedure for monitoring, reporting and correction of adverse drug interactions was conducted in the inpatient setting. One of the inputs in this study was the number of drugs administered to the patients. The investigator took a random sample of 92 patients from a list of all patients ever admitted to the hospital within a three-month period and the number of drugs prescribed per admission was determined for each. It was found that there were 7.6 average drugs per case. [1] What is the parameter being estimated? [2] What is the point estimate of this population parameter? [3] If the investigator computed a standard deviation of 1.13, construct and interpret a 95% and a 99% confidence interval estimate for the parameter being estimated?

Learn how to estimate the population mean of drugs prescribed per admission in a tertiary hospital using sample data. This problem involves calculating point estimates, constructing 95% and 99% confidence intervals, and applying statistical concepts such as the confidence interval formula and Central Limit Theorem. Suitable for students in Grades 11-12.

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