Question

A survey of recent graduates of Bachelor's degrees showed that 142 smoke and 508 do not smoke.

Estimate the value of the true proportion that smoke using a point estimate.

Determine a 95% confidence interval for the true proportion of recent graduates of Bachelor's degrees that smokes.

95% CI: ANSWER to ANSWER

Answer 1

Given : p^ = 142/(142 + 508) = 0.2185.

1 - p^ = 508/(142 + 508) = 0.7815.

z for 95% = 1.96.

LCL = p^ - z √(p^ * (1 - p^) / n)

= 0.2185 - 1.96 * √(0.2185 * 0.7815 / (142 + 508))

= 0.1867.

UCL = p^ + z √(p^ * (1 - p^) / n)

= 0.2185 + 1.96 * √(0.2185 * 0.7815 / (142 + 508))

= 0.2503.

The confidence interval is 0.1867 to 0.2503.