Questions: 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 β̄ ? μβ̂=p=0.12 μp̂=np=100(0.12)=12 μp̂=1-p=1-0.12=0.88 μp̂=n(1-p)=100(1-0.12)=88

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 β̄ ?
μβ̂=p=0.12
μp̂=np=100(0.12)=12
μp̂=1-p=1-0.12=0.88
μp̂=n(1-p)=100(1-0.12)=88

Transcript text: 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 $\bar{\beta}$ ? $\mu_{\hat{\beta}}=p=0.12$ $\mu_{\hat{p}}=n p=100(0.12)=12$ $\mu_{\hat{p}}=1-p=1-0.12=0.88$ $\mu_{\hat{p}}=n(1-p)=100(1-0,12)=38$

Solution

Solution Steps

Step 1: Identify the parameter of interest

The parameter of interest is the proportion of twins born in the town, denoted as $ p = 0.12 $.

Step 2: Understand the sampling distribution

The sampling distribution of the sample proportion $ \hat{p} $ has a mean equal to the population proportion $ p $. This is a fundamental property of the sampling distribution of proportions.

Step 3: Calculate the mean of the sampling distribution

The mean of the sampling distribution of $ \hat{p} $ is given by: \[ \mu_{\hat{p}} = p = 0.12 \]