The 95% confidence interval is:
(a) Larger than the 99% confidence interval
(b) Smaller than the 99% confidence interval
(c) The same as the 99% confidence interval
It means the range of a variable, centered at the most likely mean value, that the variable is in 95% of the time. The range that the variable is 99% of the time is wider. Therefore the answer is (b)
Thanks...
So the following would be b as well:
For two normal distributions with the same mean, but different standard deviations, the 95% confidence interval will be:
(a) The same for both distributions
(b) Larger for the distribution with the smaller standard deviation
(c) Smaller for the distribution with the smaller standard deviation
95% confidence interval is approximately 2 standard deviations (SDs) away from the mean in each direction (�}2 SD). Do you still believe that the 95% confidence interval would be larger for a smaller SD?
I hope this helps. Thanks for asking.
To determine whether the 95% confidence interval is larger, smaller, or the same as the 99% confidence interval, we need to understand what these confidence intervals represent.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The level of confidence represents the probability that the true parameter falls within the interval.
In this case, the 95% confidence interval means that if we were to repeat the same sampling process and construct a confidence interval 100 times, approximately 95 of those intervals would contain the true population parameter. Similarly, the 99% confidence interval means that approximately 99 of 100 intervals would contain the true parameter.
Since the level of confidence for the 99% confidence interval is higher than that of the 95% confidence interval, it means that with a higher confidence level, the interval needs to be wider to account for the increased variability and uncertainty.
Therefore, the correct answer is (a) The 95% confidence interval is larger than the 99% confidence interval.