Final answer:
The statement is true; a 99% confidence interval is wider than a 95% one and would include the same values plus additional ones for higher confidence. A 90% confidence interval does not contain 90% of data, but rather means there's a 90% chance that the interval contains the true mean. Lowering the confidence level from 99% to 90% narrows the interval.
Step-by-step explanation:
The statement that if a given value is within a 95% confidence interval, it will also be within a 99% confidence interval is true. This is because a 99% confidence interval is wider than a 95% confidence interval, and thus encompasses more potential values. It's designed to provide a higher level of certainty (or confidence) that the interval contains the true parameter value, so it includes the same values the 95% interval does, plus some additional ones on either side to account for the increased confidence level.
When constructing a 90 percent confidence interval, saying that we're 90 percent confident that the true population mean lies within the interval means if we were to take many samples and create a confidence interval from each one, we would expect 90% of those intervals to contain the true population mean. It does not mean that 90 percent of the data lies within the interval, but rather that there's a 90 percent chance our interval includes the true mean.
If the confidence level is decreased from 99 percent to 90 percent, the confidence interval would become narrower. This happens because we are accepting a lower level of confidence for the interval containing the true parameter, allowing us to say that it excludes more of the distribution (from 1% to 10% with the decrease).