A proponent of a new proposition on a ballot wants to know the population percentage of people who support the bill. Suppose a poll is taken, and 540 out of 1000 randomly selected people support the proposition. Should the proponent use a hypothesis test or a confidence interval to answer this question? Explain. If it is a hypothesis test, state the hypotheses and find the test statistic, p-value, and conclusion. Use a $2.5 \%$ significance level. If a confidence interval is appropriate, find the approximate $95 \%$ confidence interval. In both cases, assume that the necessary conditions have been met.
C. Do not reject $\mathrm{H}_{0}$. There is not enough evidence to conclude that the proposition will pass.
D. Do not reject $\mathrm{H}_{0}$. There is enough evidence to conclude that the proposition will pass.
E. A hypothesis test is not the most appropriate approach. The proponent should use a confidence interval.

If a confidence interval is the most appropriate approach, construct an approximate $95 \%$ confidence interval for the population proportion p of voters in favor of the proposition. Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
A. ( $\square, \square$
(Round to three decimal places as heeded.)
B. A confidence interval is not the most appropriate approach. The proponent should use a hypothesis test.

Step 1 ：The question is asking whether a hypothesis test or a confidence interval is more appropriate for determining the population percentage of people who support a proposition. It also asks for the calculation of the test statistic, p-value, and conclusion if a hypothesis test is appropriate, or the calculation of the 95% confidence interval if a confidence interval is appropriate.

Step 2 ：Given that the proponent wants to know the population percentage of people who support the bill, a confidence interval would be more appropriate. A confidence interval provides a range of values, derived from the sample, that is likely to contain the population parameter. A hypothesis test, on the other hand, is used to test a claim about a population parameter based on a sample statistic.

Step 3 ：To calculate the 95% confidence interval for the population proportion, we can use the formula for the confidence interval for a proportion, which is: \[\hat{p} \pm z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\] where \(\hat{p}\) is the sample proportion, \(z\) is the z-score corresponding to the desired confidence level (for a 95% confidence level, \(z\) is approximately 1.96), and \(n\) is the sample size.

Step 4 ：In this case, \(\hat{p} = \frac{540}{1000} = 0.54\), \(z = 1.96\), and \(n = 1000\).

Step 5 ：Calculate the standard error (se) using the formula \(se = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\), which gives \(se = 0.015760710643876435\).

Step 6 ：Calculate the lower and upper bounds of the confidence interval using the formula \(\hat{p} \pm z \times se\), which gives \(ci_{lower} = 0.5091090071380022\) and \(ci_{upper} = 0.5708909928619978\).

Step 7 ：The approximate 95% confidence interval for the population proportion p of voters in favor of the proposition is \(\boxed{(0.509, 0.571)}\).