Question

Suppose it is known that 18% of adults do not have health insurance. Suppose we randomly select 120 adults and find that 15% of them do not have health insurance. Which of the following correctly describes the distribution for the proportion of adults in our sample who do not have health insurance?

	a.	p̂ ~ AN(0.18, 0.0351)
	b.	p̂ ~ AN(0.15, 0.0326)
	c.	X ~ B(120, 0.15)
	d.	p̂ ~ AN(0.15, 0.0011)

Answer 1

Answer is a.

That is the distribution for the proportion of adults in our sample who do not have health insurance , asymptotically normally distributed with mean 0.18 and standard deviation 0.0351

Calculations

We are given that population proportion is

We are selecting a random sample of 120 adults.

Here

Let be the sample proportion.

Then has asymptotic normal distribution with mean and standard deviation

Now,

Hence we have