Question

let p be the population proportion for the following condition. find the point estimates for p and q. in a survey of 1832 adults from country a, 322 said that they were not confident that the food they eat in country a is safe. the point estimate for p, p, is (round to three decimal places as needed.) the point estimate for q, q, is (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 \( p \) is \( \hat{p}=\frac{x}{n} \), where \( x \) is the number of successes (in this case, the number of people with the characteristic, which is 322) and \( n \) is the sample size (1852).

$$ \hat{p}=\frac{322}{1852}\approx 0.174 $$

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

Since \( q = 1 - p \), and we use the point - estimate relationship \( \hat{q}=1-\hat{p} \).

$$ \hat{q}=1 - 0.174=0.826 $$

Answer:

The point estimate for \( p(\hat{p}) \) is \( 0.174 \) and the point estimate for \( q(\hat{q}) \) is \( 0.826 \)