how to make a hypothesis test in statcrunch

Hypothesis Test for Mean Difference using StatCrunch

I see a lot of students struggle with recognizing what a problem statement is asking them to do. Consider this problem:

What do you get from that reading? I get:

• The phrase “Can the engineer support the claim…” tells me this is to be a hypothesis test.
• The second part of that sentence, “have different mean braking distances” indicates it is a test of the difference in means, µ d = µ 1 – µ 2 .
• That phrase also tells me the claim is “the means are different” which says the population means are not equal, µ 1 ≠ µ 2 .
• Since the null hypothesis always is a form of equality, ≤, =, ≥, the null cannot be the claim, which makes the alternative the claim.
• The alternative hypothesis is the complement of the null, so the two hypotheses are: Ho: µ 1 = µ 2 and Ha: µ 1 ≠ µ 2
• The math operator in the alternative always indicates the “tail” of the test. Here, it tells me the test is a two-tailed test.
• The fact that the standard deviations are σ’s, the population standard deviations, and not the sample standard deviations, s, tells me to run a z-test.[Note: some textbook authors say you can run the z-test without the population σ if n is > 30; other authors state you should always run the t-test if you do not have σ. As n increases beyond 30, the difference between the two tests becomes negligible but may be enough to trip you up if you are required to report answers in four decimal places. So, check with your textbook/instructor for the preference on this.]

I like to solve these types of problems using StatCrunch ® .

First, find the critical values of z using the StatCrunch normal calculator: Stat > Calculators > Normal . I prefer to use the “Between” option for two-tailed tests and enter the confidence level, c = 1- alpha, in the probability box. Here, I entered 0.9 and clicked Compute.

The resulting graph shows a red area under the curve which represents 0.9, which puts alpha/2 = 0.05 in each tail. The critical values of z are -1.645 and +1.645 and the rejection regions are z < -1.645 and z > +1.645.

Although you could solve for the test statistic manually using

and then use tables to find the p-value,

I prefer to use StatCrunch to do the entire test. Use the command sequence Stat > Z Stats > 2 Sample > With Summary .

In the dialog box that opens, enter the data for the two samples. Note: enter the population σ’s for the two samples and do not convert them  to the sample standard error (standard deviation of the sampling distribution). Although you would do this if running the test “manually,” StatCrunch is set up to do this conversion for you.

Click Compute!

The test statistic is -0.900, rounding to three decimals, and the p-value is 0.368. The test statistics does not fall in the rejection regions of <-1.645 or >+1.645, therefore the decision is to not reject the null hypothesis. That is the same result the p-value tells us since it is > alpha = 0.1.

Since the alternative is the claim, I would state my conclusion as:

At the 10% significance level, there is not enough evidence to support the claim that the mean braking distance for Type 1 tires is different than Type 2 tires.

Remember, you can quickly get the confidence interval around the mean difference by clicking on the Options button at the top left of the Output window, and click on Edit. Options > Edit. Then change select Confidence Interval for µ 1 – µ 2 and enter the confidence level desired. Then, click Compute!

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• Knowledge Base

Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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