Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 19 - Estimating a Population Proportion (2 of 3 discussion 1)

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2026-01-17T21:14:49-08:00

Answer to Number 1: 95% confidence interval

(60%) and

Conditions: With such a large sample, we obviously have more than 10 successes and failures. There are (1019)(0.60) about 611 successes and (1019)(0.40) about 408 failures. So we can use the confidence interval formula.

Calculating the 95% confidence interval:

0.60 ± 2 (0.015)

0.60 ± 0.030, which gives the interval 0.57 to 0.63

Answer to Number 2: 90% confidence interval

The only thing that changes is the margin of error. Instead of 2 standard errors, the 90% confidence interval has a margin of error equal to 1.65 standard errors.

0.60 ± 1.65(0.015)

0.60 ± 0.025, which gives the interval 0.575 to 0.625.

Answer to Number 3: Which has a smaller margin of error?

The 90% confidence has a smaller margin of error. We can see this in the calculations; the margin of error is 1.65 times the standard error instead of 2 times the standard error.

Answer to Number 4: Which is more likely to contain the population proportion?

The 95% confidence interval is more likely to contain the population proportion. The confidence level describes the chance (probability) that the associated confidence interval will contain the population proportion. With a 95% confidence interval, there is a 95% chance that the interval contains p; while the 90% confidence interval has a 90% chance of containing p.