A word of caution: i'm using loose logic and vocabulary here to arrive at the answer...
> A random sample of size n is collected from a population, and from the > data collected a 95% confidence interval for the mean of the > population is computed.. Which of the following changes in condition > would definitely result in a confidence interval with a smaller width > than the one computed. > > A - and increased in the population standard deviation unlikely since an increase in the standard deviation of a fixed sample from a population means you know even less about a particular number within that sample. so, this would not decrease the width of your confidence interval. > B - a decrease in the confidence level requested from 95% - 90% the 95% confidence interval is the interval within which "one might expect to find 95% of all possible deviations from the mean in a sample"; by decreasing the confidence level, we are saying that "its ok that if only 90 out of every 100 guesses for the mean are within the interval we specify, rather than 95 out of every 100." So this would result in a decrease in the confidence interval width, because we are "tightening our beliefs that the mean is a particular value without having any additional evidence, i.e., more samples, that indicate that the mean is a particular value". Having no additional samples to cause the distribution to become more 'peaked' towards a particular value of the mean, this would reduce the interval width (i.e., the 95% to 90%). So, in summary, this is the choice i'd pick... I could be completely wrong, but it makes sense to me. > C - A decrease in the size of the sample obtained A decrease in the size of the sample should lead to the opposite effect -- you would have less confidence in your predictions about population parameter estimates based on this sample. > D - All of the above certainly not. > E - None of the above if B is right, then E can't be. Please correct me if i'm wrong. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
