When you say wider, I assume that you are implying further from the mean. The percentage of the confidence interval is representative of the percentage of all possible sample statistics lying under the sampling distribution up to the particular z or t score which corresponds to that percentage. The specifics depend on if you are doing a one or two tailed test, but the step up to 99% confidence will always mean that your sample statistic will have to be further from the mean to disprove the null hypothesis than a 95% interval. Good Luck.

A confidence iterval is a random thing, and as such, has no constant width. On average, the 99% interval cannot be more narrow than the 95% interval, since 99% is greater than 95%. If a random interval covers the true, constant but unknown, value of the corresponding parameter with the probability of 99%, it certainly covers it with any other smaller probability. Therefore, it already IS a 95% CI. Of course, from the point of view of common sense this sounds somewhat weird; it is like if you ask me whether I have a dollar and I say yes, but I know that actually there is a hundred bucks in my pocket. In cases of commonly used distributions like the normal, the binomial, etc., to actually increase the probability of coverage you need to increase the interval width (again, the average width!). However, it is easy to imagine an exotic distribution, for which the same intervals cover the unknown parameter values with any probability from 95% to 99%. All the above is about the theory. In real life you DO NOT deal with confidence intervals as random objects; you deal with their particular realizations calculated based on a specific, fixed - since it has been drawn already - and therefore non-random sample. If you are using the same sample for calculating realizations of both the 95% and 99% intervals, the 99% one will be inevitably wider, since sample estimates of the mean, the standard deviation, or whatever, will be the same in both cases, but the statistical coefficents like t, z, etc., grow as the confidence probability - which you choose as you please, to satisfy your needs - grows. If, however, you are using two different samples, one for 99% and the other for 95%, it is quite possible that the sampling value of the, say, standard deviation in the first case happens to be so much smaller than the same value for the second sample (remember, both are particular realizations of a random value!), that even after multiplying by the corresponding statistical coefficient the 99% realization of the CI gets to be more narrow than the 95% realization. Confidence intervals are not so simple! However, in reality you do not deal with those random

Confidence level (CL) and confidence interval (CI) are intimately related. One without the other is meaningless. Let's say I flip a fair coin 100 times. The expectation value for the number of heads after 100 flips is 50. What does this mean? Does it mean that every time I flip a coin 100 times, I'll get 50 heads? No, of course not, I could get 49 heads, or 45, and there's even a small chance I'll get a run of 100 straight heads. Expectation value means that if I do the experiment (we define the experiment as "flip a coin 100 times") an infinite number of times, *on average*, the number of heads for each experiment will approach 50. Some of the trials of this experiment will certainly be far from 50, however. Obviously, it's impossible to actually do this experiment an infinite number of times, but it should be clear that the more trials of the experiment we run, the closer we'll get to the average of 50 heads per trial over all the trials. Now the question becomes--how many trials of this experiment do we have to run to get reasonably close to 50? First, we have to define what we mean by "reasonably close". This is the "confidence interval". For the purposes of this example, let's say we want to be within 2 heads of 50, so between 48 and 52 is close enough, so the confidence interval we're interested in is 4. It's not enough to define the CI, however. We also need to define a confidence level. In other words, we have to accept that, no matter how many times we run this experiment, in some cases it may take a very, very long time for the actual average to land within 2 heads of 50, and in other cases, it might happen on the first trial. So, we want to settle on a number of trials that will guarantee we land in our defined CI some percentage of the time. This percentage is our CL. Let's say that we want to be 95% confident that we'll repeat the experiment enough times that the average will land in our CI. Now how do we figure out the number of trials we need to run to satisfy a 95% CL with a CI of 4? (This is where the formulas come in.) So we plug in the numbers and come up with a number of trials n we must execute that will satisfy our confidence parameters. We understand that, if we do this experiment n times (whatever n comes out to be), 5% of the time the average number of heads will fall outside our CI because we've only chosen a 95% CL. Without changing n, we might want to say, ok, what CI can we be 99% confident in, then? Obviously, if we plug in a CL of 99% and leave n the same, the CI is going to grow. In other words, whereas we were 95% our average would land in +/-2 of 50 heads if we run it n times, we might find that we'll be 99% confident the average will fall into a CI of +/-6. The more we raise the confidence level, the wider the CI must grow to compensate. Similarly, if we decide to narrow the CI without changing the number of trials n, we find that we're less and less confident of landing in that CI with only n trials. If we narrow the CI to +/-1, we might find we're only 85% confident (in other words, 15% of the time we run the experiment, the actual measured average will be outside our new CI of +/-1). If we set the CI to be very small, say +/-0.1 (remember, it's an average of the number of heads over n trials, so this can be fractional), we might find our confidence level plummet to 10%, meaning 90% of our experiments will yield an average number of heads less than 49.9 or greater than 50.1. Typically, we set confidence intervals around the expectation value because that is the value that repeated trials will approach. It's sometimes useful, however, to define a condition that is not interested in the mean. For instance, we might not be concerned with the average number of heads over n trials--we might instead be interested in the following question: How many trials do we have to run before we get a single result of 75 heads? Of course, once again, we find that the question is unanswerable--we may run that experiment a million times and never get exactly 75 heads. We can never be 100% sure for any given trial that we'll get a result of 75 heads. But, we can ask the question slightly differently. How many times do we have to run the experiment to be 99% confident that at least one trial will have 75 heads out of 100 flips, with a CI of 1 (between 74.5 and 75.5--since the number of heads is an integer, this CI will give us the number of trials for exactly 75 flips if we're using a continuous distribution...if we use a discrete distribution, then we can simply say 75 heads exactly). This is exactly the kind of math that concerns the Vegas gambler. How many times do I have to bet on double-0 at that roulette wheel before I'm 99% confident that I'll win? How much money will I have spent on average doing this, and how much will I win? You can bet that the house will set the odds such that the average amount spent on this experiment will always be slightly higher than the amount won. Gamblers are a superstitious lot, and they believe they can change their luck in all sorts of strange ways. If you want proof that these superstitions are ineffective, just look at the house's strategy. They change their luck in one way and one way only--by running as many trials as humanly possible. They know that the odds are in their favor, but only if they run a large number of trials. The more they run, the closer the numbers converge to the expectation values, and the more volume they do, the more money they make. So the next time a gambler tells you he has a superstition that he believes changes his luck, you can feel confident that the revenue sheets of the casino he's gambling in is proof to the contrary.