Question

In a random sample of 2000 likely voters, 1308 felt that the economy's state was the most urgent national concern. The standard error SE of p, the estimated proportion viewing the economy's state as most urgent, is:

a) 0.0001
b) 0.0312
c) 0.0106
d) 0.4926

Answer 1

The standard error (SE) of the estimated proportion (p) that views the economy's state as the most urgent national concern for a sample of 2000 voters with 1308 affirming this concern, is calculated using the formula SE = sqrt((p'(1 - p')) / n).

Step-by-step explanation:

The question asks to calculate the standard error (SE) of the estimated proportion (p) that views the economy's state as the most urgent national concern. Given a random sample of 2000 likely voters, where 1308 identified the economy as the most urgent issue, we can calculate the proportion p' and use it to find the standard error. The formula to calculate the standard error of a proportion is SE = sqrt((p'(1 - p')) / n), where p' is the sample proportion and n is the sample size.

First, calculate the sample proportion:

• p' = 1308 / 2000 = 0.654

Next, use the formula to calculate SE:

• SE = sqrt((0.654 * (1 - 0.654)) / 2000)
• SE = sqrt((0.654 * 0.346) / 2000)
• SE = sqrt(0.226524 / 2000)
• SE = sqrt(0.000113262)
• SE ≈ 0.0106

Therefore, the standard error of the estimated proportion is approximately 0.0106, which corresponds to option c).