Enter your data in the blue cells and the answers will be in the yellow cells.
Many students struggle to find critical values of z, t, and Chi-square for hypothesis tests. No matter how often I show them how to use the StatCrunch calculators to do this, they gravitate back to the tables. And make a lot of mistakes. To help a bit, I have created some Excel calculators that should make it a bit easier. A minimum of data/info is needed to use the calculators. First, you need to know which distribution you need and I have covered this in other posts. For the z, you just need to know alpha and the tail of the test which is always indicated by the math operator in the alternative hypothesis. For the t, things get a bit more complicated as you also need to know the sample size(s) and whether or not the variances are assumed to be equal if you are dealing with a two-sample test. Note you can use these calculators to find the degrees of freedom for the different tests too.
I have embedded the Critical Values workbook below. In each, you enter your data in the blue cells and all answers show up in yellow cells. In some, you will need to select options in an orange cell. As an example of how they work, here is how to use the Two Independent Samples Critical Values calculator:
This is the index of calculators.
Enter your data in the blue cells and the minimum sample size will be in the yellow cell at the bottom. Note: the standard deviation and E must be in the same units (e.g. inches, feet, etc).
Download a copy of the workbook Min Sample Size for Mean CI V1.00
If you are conducting a survey, you will need to decide on the number of people you need to sample. That, of course, depends upon how confident you want to be and how accurately you want to predict the population proportion based on your survey results. If you want to be 95% confident, that is your level of confidence, C. If you want the population proportion within + or – 2%, that is the margin of error, E, you will accept. With that information, you can find the minimum number of people to be surveyed.
If you have an estimate of the population proportion, use that as p-hat. If you do not have any prior information, use 0.5 as your initial estimate of p-hat as that will give you the largest minimum sample size.
You can do that using StatCrunch (here), but I find it quicker to use my Excel calculator below. Just enter your data in the blue cells and the answer will be in the yellow cell.
Here is the answer to part a, with no prior estimate of p-hat. The sample size is 752.
If you use the estimate of 0.34 instead of 0.5, the minimum sample size decreases to 675. The sample size decreased, which is what you should expect. Using 0.5 as the estimate when you don’t have other information will give the largest sample size.
Download a copy of the workbook here: Minimum Sample Size for Proportion CI V1.00
Problem 6.3.27 gives you some summary data about a survey and asks you to find the confidence interval for the population proportion if the margin of error, E, is also given. Although you can do this problem using StatCrunch, I find it to be one of those problems where Excel is quicker and easier, particularly if you use my “calculator.” Enter your summary data and the E. Find the answers in the yellow cells below. You may also download a copy of this workbook.
Download a copy Confidence Level for Proportion CI V1.00