Final answer:
The statement is true; a 95% confidence interval will have more data points than an 80% confidence interval because it is wider and thus designed to increase the likelihood of containing the true population parameter.
Step-by-step explanation:
For any given distribution, the statement that a 95% confidence interval will always have more data points than an 80% confidence interval is true. A confidence interval provides a range within which we can say with a certain level of confidence that the true parameter of the population lies. The wider the interval, the more data points it will likely contain.
Confidence intervals are based on the central limit theorem and are typically constructed to contain the true population parameter a certain percentage of the time if we were to take repeated samples from the population. For example, a 95% confidence interval captures the true mean 95% of the time, excluding 5% of the distribution, whereas an 80% confidence interval would exclude 20% of the distribution, making it narrower.
As the level of confidence increases, the confidence interval necessarily becomes wider to ensure a higher probability that the interval includes the true population parameter. For instance, a 99% confidence interval would be even wider than a 95% confidence interval because it aims to include all but 1% of the distribution. Therefore, the 95% confidence interval will be narrower compared to a 99% interval, but wider than an 80% interval.
Therefore answer is b. false.