Final answer:
The correct answer is option B. False. Confidence intervals should be calculated with high accuracy in intermediate steps and the final answer should have one more decimal place than the original data.
Step-by-step explanation:
The correct answer is option B. False. The statement in the question is a common misconception. When computing a confidence interval for a population mean using raw data, it is not necessary to round off to two more decimal places than the number of decimal places in the original data. Instead, a simple way to round off answers is to carry your final answer one more decimal place than was present in the original data, while intermediate calculations should be kept as accurate as possible. This practice helps to minimize rounding errors that could affect the confidence interval's accuracy.
Regarding the confidence interval itself, when we say that we have a 90% or 95% confidence interval, it means we're 90% or 95% confident that the interval contains the true population mean. If the sample size increased from 30 to 50, typically, the confidence interval would become narrower, assuming a consistent sample mean and variability, due to decreased standard error.
It's important to understand these concepts as they relate to statistical inference and how we interpret the confidence level and the range of the confidence interval in context to the sample mean and true population mean.