Question

Determine 99% confidence limits for the proportion of current residents of a city favouring the construction of a new civic arena.

Answer 1

The 99% confidence limits for the proportion of current residents favoring the construction of a new civic arena range from [lower limit] to [upper limit].

Step-by-step explanation:

To determine the 99% confidence limits for the proportion, a statistical method such as a confidence interval can be employed. This involves calculating the standard error of the sample proportion and then using it to construct the interval. The formula for the confidence interval is:

`\[ \text{Confidence Interval} = \hat{p} \pm Z * \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]`

where
`\(\hat{p}\)` is the sample proportion, (Z) is the z-score corresponding to the desired confidence level (in this case, 99%), and (n) is the sample size.

In this context,
`\(\hat{p}\)` would be the proportion of residents in favor of the new civic arena, (Z) would be the critical z-value for a 99% confidence level (which is approximately 2.576), and (n) would be the total number of respondents or the sample size.

Plugging in these values into the formula yields the lower and upper limits of the confidence interval.

In summary, the 99% confidence limits provide a range within which we are 99% confident that the true proportion of residents favoring the construction of a new civic arena lies based on the sample data collected.

This statistical measure helps quantify the uncertainty associated with estimating population parameters from a sample.