Question

let p be the population proportion for the following condition. find the point estimates for p and q.
a study of 4781 adults from country a, 2729 think mainstream media is more interested in making money than in telling the truth.
the point estimate for p, \\( \hat { p } \\), is \\( \square \\).
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the point estimate for \( p \)

The formula for the point estimate of the population proportion \( p \), denoted as \( \hat{p} \), is \( \hat{p}=\frac{x}{n} \), where \( x \) is the number of successes (in this case, the number of adults who think mainstream media is more interested in making money than in telling the truth) and \( n \) is the sample size.
Here, \( x = 2729 \) and \( n=4781 \). So, \( \hat{p}=\frac{2729}{4781}\).
Using a calculator, \( \frac{2729}{4781}\approx0.571 \).

Step2: Calculate the point estimate for \( q \)

The formula for the point estimate of \( q \) (where \( q = 1 - p \)) is \( \hat{q}=1-\hat{p} \).
Since \( \hat{p}\approx0.571 \), then \( \hat{q}=1 - 0.571=0.429 \).

Answer:

The point estimate for \( p\), \( \hat{p}\), is \( 0.571 \). The point estimate for \( q\), \( \hat{q}\), is \( 0.429 \).