Question

my virtual academy... box plot graph. box... next post test: inferences from data 22 select the correct answer from each drop - down menu. a veterinarians office recorded one particular week that they had 50 patients. the table shows the recorded number of dogs. monday tuesday wednesday thursday friday 7 4 5 5 2 use the given data to complete the sample proportion and confidence intervals for this situation. percentage of patients that were dogs 46% 90% confidence interval 95% confidence interval (6%, 23%) (34%, 60%) (32%, 60%) (5%, 21%) reset next

Explanation:

Step1: Calculate sample proportion

The total number of dogs is $7 + 4+5 + 5+2=23$. The total number of patients is $n = 50$. The sample - proportion $\hat{p}=\frac{23}{50}=0.46$ or $46\%$.

Step2: Calculate standard error for proportion

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

Step3: Find z - values for confidence intervals

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 90% confidence interval is approximately $(0.344,0.576)$ or $(34\%,58\%)$.
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 95% confidence interval is approximately $(0.322,0.598)$ or $(32\%,60\%)$.

Answer:

90% confidence interval: (34%, 60%)
95% confidence interval: (32%, 60%)