Final answer:
A biased statistic does not average to the true population parameter; rather, it systematically overestimates or underestimates that parameter. An unbiased statistic will, on average over many samples, equal the population parameter. Whether a statistic is biased or not is unrelated to the percentage of confidence intervals that contain the true parameter.
Step-by-step explanation:
False. A biased statistic means that the statistic does not accurately estimate the true population parameter. Instead, a biased statistic consistently overestimates or underestimates the value. In contrast, an unbiased statistic means that the expected value of the statistic is equal to the population parameter; in other words, it's accurate on average over many samples. Examples of unbiased statistics include the sample mean when estimating a population mean or the sample proportion when estimating a population proportion.
According to the central limit theorem, the larger the sample, the more the sampling distribution of the sample mean will look like a normal distribution and center over the true population mean. This distribution is centered on the true population parameter only if the statistic is unbiased. However, while confidence intervals constructed around this mean can contain the true population parameter with a certain level of confidence (for example, 90% or 95% of the time), this is not indicative of whether the statistic itself is biased or not.
In summary, the mean of a sampling distribution of the means might be approximately the mean of the data distribution, but this does not confirm bias or lack thereof. Only when the averages are consistently centered over the true population parameter after repeated sampling, can we consider a statistic to be unbiased.