True or false? If the original x distribution has a relatively small standard deviation, the confidence interval for will be relatively short.
Answer
True
False
I think it is true.
Confidence interval = mean ± (number of standard deviations) SD
I agree.
False.
Explanation: The length of a confidence interval is primarily determined by the sample size and the level of confidence, not the standard deviation of the original distribution. A smaller standard deviation means that the data points in the original distribution are clustered closer to the mean, which can lead to a more precise estimate of the population parameter. However, this does not directly affect the length of the confidence interval.