Question

eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting for, either north high school or south high school. from the results of his survey, eric obtained a 95% confidence interval of (0.52, 0.68) for the proportion of all adults in the city rooting for north high. what proportion of the 150 adults in the survey said they were rooting for north high school?
choose the correct answer below.
○ a. 0.646
○ b. 0.60
○ c. somewhere between 0.52 and 0.68, but the exact proportion cannot be determined
○ d. this information cannot be determined from the information given in the problem.

Explanation:

Step1: Recall the formula for a confidence interval

The formula for a confidence interval for a proportion is $\hat{p}\pm z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, where $\hat{p}$ is the sample proportion. The mid - point of the confidence interval $(a,b)$ is given by $\hat{p}=\frac{a + b}{2}$.

Step2: Calculate the mid - point of the given confidence interval

Given the confidence interval $(0.52,0.68)$, we use the formula for the mid - point. Substitute $a = 0.52$ and $b=0.68$ into the formula $\hat{p}=\frac{a + b}{2}$. Then $\hat{p}=\frac{0.52+0.68}{2}=\frac{1.2}{2}=0.60$.

Answer:

B. \(0.60\)