Question

According to the National Institute of Health, about 37% of high school seniors have vaped in the past year. Suppose that a survey contacts an SRS of 400 high school seniors and calculates the sample proportion, , in this sample who have vaped in the past year. What is the mean of the sampling distribution of ?

Answer 1

Using the Central Limit Theorem, it is found that the mean of the sampling distribution of sample proportions is 0.37.

The Central Limit Theorem establishes that, for a proportion p in a sample of size n, the sampling distribution of sample proportions has:

• Mean $\mu = p$.

• Standard error $s = \sqrt{\frac{p(1 - p)}{n}}$

For this problem, about 37% of high school seniors have vaped in the past year, hence $p = 0.37$.

• Then, the mean of the sampling distribution of sample proportions is 0.37.

For more on the Central Limit Theorem, you can check brainly.com/question/4086221