If you have one small set of data (under 30 items), you’ll want to use the t-distribution instead of the normal distribution to construct your confidence interval. Step 1: Subtract the confidence level (Given as 95 percent in the question) from 1 and then divide the result by two. The formula might look daunting, but all you really need are two pieces of information: the z-score and the P-hat.
Step 2: Look up the value you calculated in Step 1 in the z-table and find the corresponding z-value. Finding confidence intervals for two populations can look daunting, especially when you take a look at the ugly equation below. It looks a lot worse than it is, because the right side of the equation is actually a repeat of the left!
Example question: A study revealed that 65% of men surveyed supported the war in Afghanistan and 33% of women supported the war. The TI 83 allows you to find a CI for the difference between two means in a matter of a few keystrokes. Sample problem: A recent poll shows that 879 of 1412 Americans have had at least one caffeinated beverage in the last week.
If you don’t know how to enter data into a list, you can find the information in this article on cumulative frequency tables. Sample problem #2: A recent poll in a simple random sample of 986 women college students found that 699 agreed that textbooks were too expensive. A 95% confidence level means is that if the survey or experiment were repeated, 95 percent of the time the data would match the results from the entire population. A 95% confidence interval gives you a very specific set of numbers for your confidence level. But in reality, most confidence intervals are found using the t-distribution (especially if you are working with small samples). It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound!).
With any survey or experiment, you’re never 100% sure that your results could be repeated.

Check out our statistics how-to book, with a how-to for every elementary statistics problem type.
This section breaks everything down into simple steps and shows you how to find a confidence interval for population proportions.
You should be familiar with looking up z-scores from previous sections on the normal distribution (if you need a refresher, be sure to watch the above video) and P-hat is just dividing the number of events by the number of trials.
Finding confidence intervals for two populations can be broken down to an easy three steps.
If 100 men and 75 women were surveyed, find the 90% confidence interval for the data’s true difference in proportions. Instead of a single number for the mean, a confidence interval gives you a lower estimate and an upper estimate. For example, if there’s a new drug being tested for diabetes, researchers might be interested in comparing the mean blood glucose level of the new drug takers versus the mean blood glucose level of a control group. Enter the values from the problem into the appropriate rows, using the down arrow to switch between rows as you complete them.
Successes in this question is how many Americans have had at least one caffeinated beverage (879). You’ll need the graphlink cable that came with your calculator to transfer the software.
If you aren’t sure which technique you should be looking at, start with #1 below (how to find a confidence interval for a sample). It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Find a confidence interval for a sample for the true mean weight of all foot surgery patients. See this article, area to the right of a z-score for an explanation on how to read the z-table. Over the long-term, if you ran tests on many, many samples, there is a 99 percent probability that the calculated intervals would contain the true mean. The confidence interval(CI) for the difference between the two population means is used to assist researchers in questions such as these.

This means that you are 95% confident that between 54% and 65% of the student body agree with your decision.
What is the 95% confidence interval for the difference in proportions between the two populations? Having a 95% confidence level means that you’re almost certain your results are the same as if you had surveyed everyone.
For example, you survey a group of pet owners to see how many cans of dog food they purchase a year.
That means if you repeated this over and over, 95 percent of the time the scores would fall somewhere between 780 and 900.
You test your statistics at the 99 percent confidence level and get a confidence interval of (200,300). The equations involved in statistics often involve a lot of minor calculations (such as summation), plus you would also need to calculate the margin of error and the mean of the sample. If your results fall into the red region, then that’s outside of the 95% confidence level that you, as a researcher, set.
It’s very easy for errors to slip in if you calculate the confidence interval by hand.
You’re super confident (99% is a very high level!) that your results are sound, statistically. However, Excel can calculate the mean of the sample, the margin or error and confidence interval for the mean for you. All you have to do is provide the data — which for this technique must be a sample greater than about 30 to give an accurate confidence interval for the mean.

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