Question

the proportion of twins born in a town is ( p = 0.12 ). suppose we randomly select 100 women from this town who give birth in the next year. which of the following is the mean of the sampling distribution of ( hat{p} )?
( mu_{hat{p}}=p = 0.12 )
( mu_{hat{p}}=np = 100(0.12)=12 )
( mu_{hat{p}}=1 - p = 1 - 0.12 = 0.88 )
( mu_{hat{p}}=n(1 - p)=100(1 - 0.12)=88 )

Explanation:

Step1: Recall the formula for the mean of the sampling distribution of \(\hat{p}\)

The mean of the sampling distribution of the sample proportion \(\hat{p}\), denoted as \(\mu_{\hat{p}}\), is equal to the population proportion \(p\). Mathematically, \(\mu_{\hat{p}}=p\).

Step2: Substitute the given population proportion

We are given that \(p = 0.12\). Substituting this value into the formula \(\mu_{\hat{p}}=p\), we get \(\mu_{\hat{p}}=0.12\).

Answer:

\(\mu_{\hat{p}}=p = 0.12\) (the first option)