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A veterinarian's office recorded that they had 50 patients in one particular week. The table shows the recorded number of dogs each day.

\begin{tabular}{|c|c|c|c|c|}
\hline Monday & Tuesday & Wednesday & Thursday & Friday \\
\hline 7 & 4 & 5 & 5 & 2 \\
\hline
\end{tabular}

Use the given data to complete the sample proportion and confidence intervals for this situation.

\begin{tabular}{|l|l|}
\hline Percentage of patients that were dogs & [tex]$\checkmark$[/tex] \\
\hline [tex]$90 \%$[/tex] confidence interval & [tex]$\checkmark$[/tex] \\
\hline [tex]$95 \%$[/tex] confidence interval & [tex]$\checkmark$[/tex] \\
\hline
\end{tabular}



Answer :

Let's go through the solution step-by-step from the given data to find the missing values for the sample proportion and confidence intervals.

1. Calculate the Total Number of Dogs:

Add the number of dogs recorded each day:
[tex]\(7 + 4 + 5 + 5 + 2 = 23\)[/tex]

2. Calculate the Sample Proportion:

Divide the total number of dogs by the total number of patients:
[tex]\[\text{Sample Proportion} = \frac{\text{Total Number of Dogs}}{\text{Total Number of Patients}} = \frac{23}{50} = 0.46\][/tex]

3. Calculate 90% Confidence Interval:

From the given data, the 90% confidence interval is [tex]\((0.34405, 0.57595)\)[/tex]

4. Calculate 95% Confidence Interval:

From the given data, the 95% confidence interval is [tex]\((0.32185, 0.59815)\)[/tex]

Summarizing these answers:
- Percentage of patients that were dogs:
[tex]\[\boxed{46\%}\][/tex]

- 90% confidence interval:
[tex]\[\boxed{(0.34405, 0.57595)}\][/tex]

- 95% confidence interval:
[tex]\[\boxed{(0.32185, 0.59815)}\][/tex]

This breakdown provides the necessary steps and values to fully answer the question based on the provided data and computations.