You asked a sample of individuals what kind of animal is their favorite. Of the 167 individuals in your sample, 52 of them answered "dog".

Which of the following gives a 95 percent confidence interval for the true percentage of individuals whose favorite animal is a dog.

Step 1 ：Given that the sample size \(n = 167\) and the number of individuals who answered 'dog' \(x = 52\).

Step 2 ：First, calculate the sample proportion \(\hat{p}\) using the formula \(\hat{p} = \frac{x}{n}\).

Step 3 ：Substitute the given values into the formula to get \(\hat{p} = \frac{52}{167} = 0.31137724550898205\).

Step 4 ：Next, calculate the standard error (SE) using the formula \(SE = \sqrt{ \frac{\hat{p} * (1 - \hat{p})}{n}}\).

Step 5 ：Substitute the values into the formula to get \(SE = \sqrt{ \frac{0.31137724550898205 * (1 - 0.31137724550898205)}{167}} = 0.03583239898883045\).

Step 6 ：Then, calculate the confidence interval using the formula \(\hat{p} \pm Z * SE\), where \(Z = 1.96\) for a 95% confidence interval.

Step 7 ：Substitute the values into the formula to get the lower and upper bounds of the confidence interval: \(CI_{lower} = 0.31137724550898205 - 1.96 * 0.03583239898883045 = 0.24114574349087436\) and \(CI_{upper} = 0.31137724550898205 + 1.96 * 0.03583239898883045 = 0.38160874752708973\).

Step 8 ：Finally, convert the confidence interval to percentages to get \(CI_{lower} = 0.24114574349087436 * 100\% = 24.1\%\) and \(CI_{upper} = 0.38160874752708973 * 100\% = 38.2\%\).

Step 9 ：The 95 percent confidence interval for the true percentage of individuals whose favorite animal is a dog is approximately \(\boxed{[24.1\%, 38.2\%]}\).