Q.1.3. - The Practice of Statistics for AP

Question

About $75\%$of young adult internet users $(ages 18-29)$ watch online video. Suppose that a sample survey contacts an SRS of $1000$ young adult Internet users and calculates the proportion of $\overbrace{p}$ in this sample who watch online video.

Is the sampling distribution of $\overbrace{p}$ approximately normal? check that the normal condition is met.

Step-by-Step Solution

Answer

The sampling distribution of $\overbrace{p}$is approximately normal.

Step-1 Given Information

Given In the question that population proportion $\left(p\right)=75\%=0.75$

Sample size $\left(n\right)=1000$

Step-2 Explanation

If the following conditions are met, the sampling distribution is considered to be nearly normal:

$np\ge 10$

$n(1-p)\ge 10$

here,

$$\begin{gathered} np=1000\left(0.75\right) \\ =750>10 \end{gathered}$$

And,

$$\begin{gathered} n(1-p)=1000(1-0.75) \\ =250>10 \end{gathered}$$