Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 201 with 38 successes at a confidence level of 80%.
To find the margin of error, we can use the formula:
M.E. = (z * √(p̂(1-p̂))/n)
where z is the critical value, p̂ is the sample proportion, and n is the sample size.
First, we need to find the critical value. Since the confidence level is 80%, we want to find the z-value that corresponds to that confidence level. Looking it up in a table, we find that the z-value for an 80% confidence level is approximately 1.28.
Next, we calculate the sample proportion p̂ by dividing the number of successes (38) by the sample size (201):
p̂ = 38/201 ≈ 0.189
Now we can plug in the values into the formula to calculate the margin of error:
M.E. = (1.28 * √(0.189(1-0.189))/201)
M.E. ≈ 0.073
Therefore, the margin of error that corresponds to a sample of size 201 with 38 successes at a confidence level of 80% is approximately 0.073.