Final answer:
The correct answer is False. The statement is false. A 95% confidence interval indicates that there is a 95% confidence level that the true population mean is within the given interval, not that 95% of the population values are within those numbers.
Step-by-step explanation:
The statement that "the 95% confidence interval for the population mean is (275, 325)" does not mean that 95% of the population values lie between 275 and 325. This is a misunderstanding of what a confidence interval represents. A confidence interval in statistics provides a range of values within which there is a specified level of confidence (in this case, 95%) that the true population parameter (like the mean) will fall. It's not about the percentage of individual data points or population values within that range; rather, it's about the certainty that the range includes the true population parameter.
To elaborate, if we say that we are 95% confident in the interval, we mean that if we were to take multiple samples and calculate a confidence interval from each of them, we would expect about 95% of those intervals to contain the true population mean. The width of the interval also plays a role; a 95% confidence interval will be wider than a 90% confidence interval because it requires more certainty about including the true mean.
Therefore, when interpreting a 95% confidence interval, one should clearly articulate that we are estimating that the true population mean lies within the given range with a 95% level of confidence. This interpretation is foundational to statistical inference and is crucial to accurately convey what confidence intervals mean in the context of statistical analysis.