Final answer:
The confidence level for an interval corresponds to the level of certainty that the interval contains the true population parameter. A higher confidence level results in a wider interval, while a lower confidence level leads to a narrower interval. The percentage within the interval does not equate to the confidence level.
Step-by-step explanation:
The question is asking for the confidence level associated with a given critical value. The critical value is not provided, but generally, confidence levels such as 70.62%, 29.38%, 14.69%, or 85.31% correspond to specific critical values that determine how wide or narrow the confidence interval is for a given set of data.
To explain this concept to someone who has not taken statistics, a confidence interval is a range of values that is likely to contain the true value of the population parameter we are estimating, such as a mean or proportion, with a certain level of confidence. For example, if we construct a 95% confidence interval for the mean height of a population from sample data, we are saying that we are 95% confident that the true population mean height falls within that interval.
It's important to note that the percentage of the data that lies within a confidence interval does not necessarily match the confidence level. For instance, if we calculate a 90% confidence interval using the heights of women in a sample, not exactly 90% of the heights will be within this interval. This is because the confidence level reflects the percentage of confidence that the interval contains the true population parameter, not the percentage of individual data points within the interval.
When a confidence level increases, such as going from 95% to 99%, the confidence interval becomes wider. This happens because we seek more certainty (a higher confidence level) that the interval contains the true value, leading to a wider range to accommodate the extra level of certainty. Conversely, if we decrease the confidence level, the interval becomes narrower.