Final answer:
The subject of this question is Mathematics. The researcher constructed a 95% confidence interval estimate of the proportion of boys in all births, using a sample size of 863 births and 423 boys. The confidence interval is 0.46 < p < 0.52.
Step-by-step explanation:
The subject of this question is Mathematics. It involves the calculation of a confidence interval to estimate the proportion of boys in all births.
Step 1: Calculate the sample proportion. In this case, the sample proportion of boys is 423/863 ≈ 0.49.
Step 2: Calculate the standard error. The formula for the standard error is √(p(1-p)/n), where p is the sample proportion and n is the sample size. Here, the standard error is √(0.49*(1-0.49)/863) ≈ 0.015.
Step 3: Calculate the margin of error. The margin of error is the product of the critical value (found using a z-table or calculator) and the standard error. For a 95% confidence interval, the critical value is approximately 1.96. Therefore, the margin of error is 1.96 * 0.015 ≈ 0.03.
Step 4: Calculate the lower and upper bounds of the confidence interval. The lower bound is the sample proportion minus the margin of error, and the upper bound is the sample proportion plus the margin of error. In this case, the lower bound is 0.49 - 0.03 = 0.46, and the upper bound is 0.49 + 0.03 = 0.52.
Therefore, the researcher constructed a 95% confidence interval estimate of the proportion of boys in all births as 0.46 < p < 0.52.