Q.3 - The Practice of Statistics for AP

Question

Going to the prom Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of $50$ of the $750$ seniors in her school and finds that $36$ plan to go to the prom 

Step-by-Step Solution

Answer

The sample proportion is $\hat{p}=75\%$. 

Step 1: Given Information

$n=\text{ Sample size }=50$

$N= Population size=750$

$x=\text{ Number of successes }=36$

Step 2: Explanation

The population proportion $p$ is estimated by the sample proportion $\hat{p}$.

The sample proportion is the number of successes divided by the sample size.

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{36}{50} \\ =\frac{18}{25} \\ =0.72 \\ =72\% \end{gathered}$$