Final answer:
To construct a 95% confidence interval for the Gallup poll result, use the standard proportion confidence interval formula, yielding an interval between 32.04% and 37.96% for Americans who believe abortion should be legal under any circumstances.
Step-by-step explanation:
The student's question revolves around constructing a 95% confidence interval for the proportion of Americans who believe abortion should be legal under any circumstances based on a Gallup poll result. To calculate the confidence interval, we use the standard formula for a proportion:
$$
CI = p \pm z*\sqrt{\frac{p(1-p)}{n}}
$$
Where:
- p is the sample proportion (0.35 in this case).
- n is the sample size (1000 respondents).
- z* is the z-score correlating to a 95% confidence level (approximately 1.96).
Plugging in the numbers:
$$
CI = 0.35 \pm 1.96*\sqrt{\frac{0.35(1-0.35)}{1000}}
$$
$$
CI = 0.35 \pm 1.96*\sqrt{\frac{0.35*0.65}{1000}}
$$
$$
CI = 0.35 \pm 1.96*\sqrt{0.0002275}
$$
$$
CI = 0.35 \pm 1.96*0.01508
$$
$$
CI = 0.35 \pm 0.02956
$$
This gives us the intervals:
$$
CI = [0.32044, 0.37956]
$$
Therefore, we are 95 per cent confident that the percent of Americans who believe abortion should be legal under any circumstances is between 32.04% and 37.96%.