Assume that the population proportion is .55. Compute the standard error of the proportion, ( ), for sample sizes of 100, 200, 500, and 1000 (to 4 decimals).
a. 100?
b. 200?
c. 500?
d. 1000?
Standard error of the proportion is:
√(pq/n)
p = .55
q = 1-p = .45
n = sample size
I'll let you take it from here.
To compute the standard error of the proportion (SEp), you can use the formula:
SEp = sqrt((p * (1 - p)) / n)
where p is the population proportion and n is the sample size.
Given that the population proportion is 0.55, and the sample sizes are 100, 200, 500, and 1000, we can compute the standard errors for each:
a. For a sample size of 100:
SEp = sqrt((0.55 * (1 - 0.55)) / 100)
= sqrt((0.3025) / 100)
≈ 0.0551
b. For a sample size of 200:
SEp = sqrt((0.55 * (1 - 0.55)) / 200)
= sqrt((0.3025) / 200)
≈ 0.0389
c. For a sample size of 500:
SEp = sqrt((0.55 * (1 - 0.55)) / 500)
= sqrt((0.3025) / 500)
≈ 0.0247
d. For a sample size of 1000:
SEp = sqrt((0.55 * (1 - 0.55)) / 1000)
= sqrt((0.3025) / 1000)
≈ 0.0172
Therefore, the standard errors of the proportion for sample sizes of 100, 200, 500, and 1000 are approximately 0.0551, 0.0389, 0.0247, and 0.0172 respectively.