Questions: According to a report, the average length of stay for a hospital's flu-stricken patients is 5.5 days, with a maximum stay of 16 days, and a recovery rate of 97%. An auditor selected a random group of 178 of the hospital's flu-stricken patients. The average stay of the audited patients was 4.8 days, their maximum stay was 14 days, and their recovery rate was 95%. (a) For the hospital audit, identify the population and the sample. Population: All the hospital's flu-stricken patients Sample: The auditor's random group of 178 of the hospital's flu-stricken patients

According to a report, the average length of stay for a hospital's flu-stricken patients is 5.5 days, with a maximum stay of 16 days, and a recovery rate of 97%. An auditor selected a random group of 178 of the hospital's flu-stricken patients. The average stay of the audited patients was 4.8 days, their maximum stay was 14 days, and their recovery rate was 95%. (a) For the hospital audit, identify the population and the sample. Population: All the hospital's flu-stricken patients Sample: The auditor's random group of 178 of the hospital's flu-stricken patients
Transcript text: According to a report, the average length of stay for a hospital's flu-stricken patients is 5.5 days, with a maximum stay of 16 days, and a recovery rate of $97 \%$. An auditor selected a random group of 178 of the hospital's flu-stricken patients. The average stay of the audited patients was 4.8 days, their maximum stay was 14 days, and their recovery rate was $95 \%$. (a) For the hospital audit, identify the population and the sample. Population: All the hospital's flu-stricken patients Sample: The auditor's random group of 178 of the hospital's flu-stricken patients
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Solution

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Solution Steps

Step 1: Identify the Population and Sample

The population refers to the entire group of individuals or instances about whom we are trying to draw conclusions. In this case, the population is all the hospital's flu-stricken patients. The sample is a subset of the population that is used to represent the population. Here, the sample is the auditor's random group of 178 of the hospital's flu-stricken patients.

Step 2: Determine Parameters and Statistics

Parameters are numerical characteristics of a population, while statistics are numerical characteristics of a sample. We need to identify which numbers in the table are parameters and which are statistics.

  • The maximum stay of 16 days among all of the hospital's flu-stricken patients is a parameter because it describes the entire population.
  • The average length of stay of 5.5 days among all of the hospital's flu-stricken patients is also a parameter for the same reason.
  • The 95% recovery rate among the auditor's random group of 178 of the hospital's flu-stricken patients is a statistic because it describes the sample.
Step 3: Fill in the Table

Based on the information above, we can fill in the table as follows:

\[ \begin{array}{|l|c|c|} \hline \text{Number} & \text{Parameter} & \text{Statistic} \\ \hline \text{The maximum stay of 16 days among all of the hospital's flu-stricken patients} & 1 & 0 \\ \hline \text{The average length of stay of 5.5 days among all of the hospital's flu-stricken patients} & 1 & 0 \\ \hline \text{The 95\% recovery rate among the auditor's random group of 178 of the hospital's flu-stricken patients} & 0 & 1 \\ \hline \end{array} \]

Final Answer

(a) Population: All the hospital's flu-stricken patients
Sample: The auditor's random group of 178 of the hospital's flu-stricken patients

(b) \(\boxed{\begin{array}{|l|c|c|} \hline \text{Number} & \text{Parameter} & \text{Statistic} \\ \hline \text{The maximum stay of 16 days among all of the hospital's flu-stricken patients} & 1 & 0 \\ \hline \text{The average length of stay of 5.5 days among all of the hospital's flu-stricken patients} & 1 & 0 \\ \hline \text{The 95\% recovery rate among the auditor's random group of 178 of the hospital's flu-stricken patients} & 0 & 1 \\ \hline \end{array}}\)

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