Question

A random sample of 860 births in a state included 398 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. The confidence interval is ( round to two four places.

Answer 1

To construct a 95% confidence interval estimate of the proportion of boys in all births, we can use the formula: p' ± Z * sqrt((p' * (1 - p')) / n). In this case, the sample proportion of boys is 398/860 = 0.4628. The Z-score for a 95% confidence level is approximately 1.96. Plugging in these values, we get the confidence interval (0.4297, 0.496).

Step-by-step explanation:

To construct a 95% confidence interval estimate of the proportion of boys in all births, we can use the formula:

p' ± Z * sqrt((p' * (1 - p')) / n)

Where:

• p' is the sample proportion
• Z is the Z-score corresponding to the desired confidence level
• n is the sample size

In this case, the sample proportion of boys is 398/860 = 0.4628. The Z-score for a 95% confidence level is approximately 1.96. Plugging in these values, we get:

0.4628 ± 1.96 * sqrt((0.4628 * (1 - 0.4628)) / 860)

Calculating this expression gives us the confidence interval (0.4297, 0.496)