# How to Do a One Sample t-test (or z-test) using the Online Calculator Wolfram Alpha

I have been a fan of Wolfram Alpha from the very beginning. While there have been some changes I am not happy with (ads – no solutions without an account), there have also been several I love. One of those is the way they have reorganized things to make some really nice online statistics calculators.

Now, there are already a few online t-test calculators out there, but none of them seems to have the same amount of information or the same “ease of use”. To show you what I mean, I am going to make up a silly example that we can try out.

The mean weight of purses carried by students at a college is thought to be less than 10 pounds. In a random sample of 35 students from this college who carried purses, the average weight was 8.3 pounds with a standard deviation of 3.9 pounds. At a significance level of 0.05, is there evidence that the mean weight for all such students is less than 10 pounds, as thought?

As you can see, we are testing a hypothesis about the mean and do not know the population standard deviation. If our data is mostly symmetric or we have a large enough sample, we can use a t-test. Usually we would talk much more about assumptions and such but for the sake of this post, we aren’t focused on the theory. So, on to the calculations!

Step 1: Go to http://www.wolframalpha.com and type in “t-test”

You can also use this direct link: Wolfram Alpha t-test Calculator

Step 2: Enter information

I completely admit that this is a much bigger step than step 1. Before we can enter any information, we need to figure out our hypotheses and what information we have. We are testing the hypothesis that the mean weight of purses for all students at this college is less than 10 pounds. This would represent an alternative hypothesis of H_{a}: \mu < 10[/latex]. In other words, our hypothesized mean is 10. Next, we look closer at the problem and see the sample mean was 8.3 pounds and the sample standard deviation was 3.9 pounds. This all came from a sample of 35 students. Since that is all gathered, we are ready to input!

Notice how a little equal appears as we input data? Clicking that takes us to step 3.

Step 3: Interpret the output

After pressing that equals sign, we will get the following screen:

(direct link: Link to this t test output in wolfram alpha)

There is actually more which you can see if you press the link above. For this problem though, we have all the information we need. Notice the default output is the p-value and test statistic for a left tailed test. This can be adjusted by clicking the right tailed test or two tailed test buttons in the upper right of the output.

But we had a left tailed test as you can see by the alternative hypothesis given. Therefore, our p-value is 0.007 < $\alpha = 0.05$ and we reject the null hypothesis. So, we do in fact have evidence to support the original belief that the average purse weight will be less than 10 pounds. We could have also made this decision using the test statistic output. As you can see in the video, it can also be used for other types of hypothesis tests! Nice!