Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

n=550 x= 220, 90% confidence

The margin of error E = (round to four decimal places)

To find the margin of error (E) for estimating the population proportion (p) with a given confidence level, you can use the formula:

E = z * sqrt((p̂ * (1 - p̂)) / n)

Where:
- E is the margin of error
- z is the z-score corresponding to the desired confidence level
- p̂ is the sample proportion (x/n)
- n is the sample size

First, calculate the sample proportion (p̂) by dividing the number of successes (x) by the sample size (n):

p̂ = x / n = 220 / 550 = 0.4

Next, find the z-score that corresponds to the desired confidence level. For a 90% confidence level, the corresponding z-score is approximately 1.645 (which you can look up in a standard normal distribution table or use a calculator).

Now, substitute the values into the formula:

E = 1.645 * sqrt((0.4 * (1 - 0.4)) / 550)

Simplifying:

E = 1.645 * sqrt((0.24) / 550)
E ≈ 1.645 * 0.0309
E ≈ 0.0508 (rounded to four decimal places)

Therefore, the margin of error (E) that corresponds to the given statistics and confidence level is approximately 0.0508.