hypothesis test on minitab

1-Sample Hypothesis Test

To add output from a 1-sample hypothesis test, go to Add and complete a form .

In This Topic

1 proportion, 1-sample wilcoxon, 1 variance test, 1-sample sign.

For example, you can test whether a new setting significantly changes the proportion defective. To see an example, go to Minitab Help: Example of 1 Proportion .

Data considerations

Your data must contain only two categories, such as pass/fail. For details, go to Minitab Help: Data considerations for 1 Proportion .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample t .

The data must be continuous and reasonably normal. A 1-sample t-test is robust to violations of the normality assumption, especially if the sample size is large (n > 25). For more details, go to Minitab Help: Data considerations for 1-Sample t .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample Wilcoxon .

Your data must be a continuous value for Y (output). The data should come from a symmetric distribution, such as the uniform or Cauchy distributions. If your data do not come from a symmetric distribution, use a 1-sample sign test. For more details, go to Minitab Help: Data considerations for 1-Sample Wilcoxon .

For example, a quality analyst uses a 1 variance test to determine whether the variance of the moisture content in a shipment of unprocessed lumber is too high. To see an example, go to Minitab Help: Example of 1 Variance .

Your data must be continuous Y (output) values. For more details, go to Minitab Help: Data considerations for 1 Variance .

For example, you can test whether the mean output from the controlled improved process is different from the pre-project mean. To see an example, go to Minitab Help: Example of 1-Sample Sign .

Use the 1-sample t-test when the data are reasonably normal (or the sample size is large).
Use the 1-sample Wilcoxon test as an alternative to the 1-sample t-test as long as the data are reasonably symmetric.
Use the 1-sample sign test as a last resort.
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6b.2 - minitab: one-sample mean hypothesis test.

Minitab ® – Conduct a One-Sample Mean t-Test

Note that these steps are very similar to those for one-mean confidence interval. The differences occur in steps 4 through 8.

To conduct the one sample mean t-test in Minitab...

Choose Stat > Basic Stat > 1 Sample t .
In the drop-down box use "One or more samples, each in a column" if you have the raw data, otherwise select "Summarized data" if you only have the sample statistics.
If using the raw data, enter the column of interest into the blank variable window below the drop down selection. If using summarized data, enter the sample size, sample mean, and sample standard deviation in their respective fields.
Choose the check box for "Perform hypothesis test" and enter the null hypothesis value.
Choose Options .
Enter the confidence level associated with alpha (e.g. 95% for alpha of 5%).
From the drop down list for "Alternative hypothesis" select the correct alternative.
Click OK and OK .

Minitab ®

Example 6-8: emergency room wait time section .

Recall our emergency room wait time example where an administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes. From our random sample of 40 patients, the average wait time for these 40 patients was 11 minutes with a standard deviation of 3 minutes. We conducted the test at a 5% level of significance and wanted to demonstrate that the average time exceeded 10 minutes. Also, recall in that example we found by hand a test statistic of t * = 2.11 and p -value with a range between 0.01 to 0.025

Our hypotheses were: \(H_0 \colon \mu=10\) and \(H_a\colon \mu>10\)

Conduct the same test using Minitab.

Using Minitab...

Select Stat > Basic Stat > 1 Sample t.
Choose the summarized data option and enter 40 for "Sample size", 11 for the "Sample mean", and 3 for the "Standard deviation".
Check the box for "Perform Hypothesis Test" and enter the null value of 10
Click Options .
With our stated alpha value of 5% we keep the default confidence level of 95.
Select "Mean> hypothesized mean" from the "Alternative Hypothesis" list.
Click OK and OK again.

The output is:

One-Sample T

Test of \(\mu\) = 10 vs \(\mu\) > 10

Again, as the output indicates, our hand calculations were quite good. Notice that Minitab provides a more exact p-value of 0.021 which corresponds to our results as it falls within our calculated range of 0.01 to 0.025.

Finding Exact Critical Value for a One-Sample Mean t-Test Section

Since the t -table is not as detailed as the z -table, we can only estimate the critical value when the degrees of freedom are not found on the table. In order to obtain the exact critical value to use in order to conduct the rejection region approach, we can use a statistical package such as Minitab.

Minitab commands to obtain critical value:

Calc > Probability Distributions > t-distribution
Choose the radio button for 'Inverse Cumulative Distribution' (this finds the t-value that produces the entered probability to the left of it).
Enter the correct degrees of freedom
Choose the radio button for 'Input constant' and enter the alpha value (if one-side alternative) or alpha/2 (if two-sided alternative).

6-8 Cont'd... Section

Find the exact critical value for our emergency room example. Recall by hand that we had to use the row with 35 degrees of freedom instead of the correct df of 39. In that example our critical value for alpha of 5% was 1.69.

Go to Calc > Probability Distributions > t-distribution .
Choose the radio button for 'Inverse Cumulative Distribution.'
Enter 39 for 'degrees of freedom.'
Choose the radio button for 'Input Constant' and enter 0.05

The output is as follows:

Student's t distribution with 39 DF

This is where you need to be a little careful. Remember that our alternative was "greater than" or a right-tailed test. The output is the critical value for a left-tailed test. However, since the t-distribution is symmetrical, the area to the left of -1.68488 would be the same as the area to the right of 1.68488. Therefore, the critical value for out test with 39 degrees of freedom would be 1.68488, which doesn't differ much from the 1.69 we estimated using 35 degrees of freedom. This is why the table skips going one by one after 30; there is little difference between the values when increasing by only one degree of freedom.

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What Statistical Hypothesis Test Should I Use?

Topics: Hypothesis Testing

So, you collected some data and now you want it to tell you something meaningful. Unfortunately, your last statistics class was years ago and you can't quite remember what to do with that data. You remember something about a null hypothesis and and alternative, but what's all this about testing?

Sometimes it's easier just to give a problem to the Assistant. Especially when it comes to statistics.

Don't get me wrong, I love to analyze data and see what it means...but most of us don't analyze data all day, every day. And in statistics, as in sports, if you don't use it, you lose it. If you haven't done an analysis in months it's not unreasonable to imagine you might need a little help.

In that case, you might seek out the Assistant. Specifically, the Assistant menu in Minitab Statistical Software . The Assistant's always ready to guide you through a difficult statistical task if you're not quite sure what to do.

The 2-Sample t-test

For example, suppose you want to compare two different materials for making backpacks –Cloth A and Cloth B –to determine which would make a more durable product. You sample materials from both suppliers and measure the mean amount of force needed to tear them.

If you're already up on your statistics, you know right away that you want to use a 2-sample t-test, which analyzes the difference between the means of your samples to determine whether that difference is statistically significant. You'll also know that the hypotheses of this two-tailed test would be:

Null hypothesis: H0: m1 - m2 = 0 (strengths of the material from both companies are equal)
Alternative hypothesis: H1: m1 - m2 ≠ 0 (strengths of the material from both companies are different)

And that if the test's p-value is less than your chosen significance level, you should reject the null hypothesis.

Maybe you're the type of person who remembers all of that stuff, even if you haven't done a t-test in years. If so, good for you–but I could stand to get a little help. Let's see what the assistant can do for me.

The Assistant and the Hypothesis Test

I'll start by pulling up Assistant > Hypothesis Tests... in Minitab. Up comes this dialog box:

Well, I know I have two samples that I want to compare. But I can't remember if I need a paired t-test, a % defective, or what. So I'll click "Help me choose." Now the Assistant gives me an easy-to-follow decision tree that leads me to the 2-sample t-test.

I can follow the tree straight to its conclusion, as shown on the right.

A Guided Path to the Right Hypothesis Test

But if I can't remember enough specifics to follow the decision tree from start to finish from the amount of information shown on the right, the Assistant will actually guide me through the process step-by-step so I arrive safely at the right hypothesis test to use.

In this scenario, The Assistant asks one question, then I choose the right option for my situation and proceed to the next question.

Particularly helpful is the fact that if I forget, for example, the difference between Continuous and Attribute data, all I have to do is click on a button and I'll get an explanation and an example for both.

In this situation, the questions I need to answer are:

Do you have continuous data or attribute data? (Answer: Continuous)
What are you comparing? (Answer: Two means)
Are you measuring different sets of items or the same set of items? (Answer: Different sets)

Now I know what test I need to use to compare the two means. But I'm not sure I know how to do that test.

Fortunately, the Assistant can help me with that, too. I'll show you how in my next post .