select the correct answer from each drop - down menu.\na veterinarians office recorded one particular week…

Explanation:

Step1: Calculate total number of dog - patients

Add the number of dogs each day: $7 + 4+5 + 5+2=23$.

Step2: Calculate sample proportion

The sample proportion $\hat{p}$ of dog - patients is $\frac{23}{50}=0.46$ or $46%$.

Step3: Calculate standard error for proportion

The formula for the standard error of a proportion is $SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, where $n = 50$ and $\hat{p}=0.46$. So $SE=\sqrt{\frac{0.46\times(1 - 0.46)}{50}}=\sqrt{\frac{0.46\times0.54}{50}}=\sqrt{\frac{0.2484}{50}}\approx\sqrt{0.004968}\approx0.0705$.

Step4: Calculate 90% confidence interval

For a 90% confidence interval, the z - value $z_{\alpha/2}=1.645$. The confidence interval is $\hat{p}\pm z_{\alpha/2}\times SE$. So $0.46\pm1.645\times0.0705=0.46\pm0.116$. The lower limit is $0.46 - 0.116 = 0.344$ or $34.4%$ and the upper limit is $0.46+0.116 = 0.576$ or $57.6%$.

Step5: Calculate 95% confidence interval

For a 95% confidence interval, the z - value $z_{\alpha/2}=1.96$. The confidence interval is $\hat{p}\pm z_{\alpha/2}\times SE$. So $0.46\pm1.96\times0.0705=0.46\pm0.138$. The lower limit is $0.46 - 0.138 = 0.322$ or $32.2%$ and the upper limit is $0.46 + 0.138=0.598$ or $59.8%$.

Answer:

Percentage of patients that were dogs: $46%$ 90% confidence interval: $(34.4%,57.6%)$ 95% confidence interval: $(32.2%,59.8%)$