Question

a simple random sample of 400 individuals provides 100 yes responses. a. what is the point estimate of the proportion of the population that would provide yes responses (to 2 decimals)? b. what is your estimate of the standard error of the proportion (to 4 decimals)? c. compute the 95% confidence interval for the population proportion (to 4 decimals).

Answer 1

a. The point estimate is 0.25 or 25%. b. The standard error is approximately 0.0212. c. The 95% confidence interval is (0.2084, 0.2916).

Step-by-step explanation:

a. The point estimate of the proportion of the population that would provide yes responses is calculated by dividing the number of yes responses (100) by the total sample size (400). In this case, the point estimate is 0.25, which can be expressed as 25%.

b. The standard error of the proportion is calculated by taking the square root of [p(1-p)/n], where p is the point estimate of the proportion and n is the sample size. In this case, the standard error is approximately 0.0212.

c. To compute the 95% confidence interval for the population proportion, we can use the formula: point estimate ± (critical value * standard error). The critical value for a 95% confidence interval is approximately 1.96. Plugging in the values, the confidence interval is calculated as 0.25 ± (1.96 * 0.0212), resulting in a confidence interval of (0.2084, 0.2916).