Question

The 95% confidence interval for a population proportion is [0.645, 0.737]. Find the standard error involved in this confidence interval. Choose the closest answer.

a) 0.046
b) 0.028
c) 0.023
d) 0.018
e) None of the above

Answer 1

The standard error involved in the given 95% confidence interval [0.645, 0.737] is approximately 0.023, which corresponds to option c).

Step-by-step explanation:

The question pertains to finding the standard error for a given 95% confidence interval for a population proportion. The 95% confidence interval provided is [0.645, 0.737]. To find the standard error, we first observe that the width of the confidence interval is 0.737 - 0.645 = 0.092. The margin of error is half of this width, which is 0.092 / 2 = 0.046. Since the standard error is directly related to the margin of error in a confidence interval calculation, and a 95% confidence interval corresponds to a Z-score (critical value) of approximately 1.96, we divide the margin of error by this Z-score to get the standard error. Calculating the standard error gives us 0.046 / 1.96 = approximately 0.023.