# Examples of Hypothesis Testing: Real-World Scenarios

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Updated September 1, 2022
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Hypothesis testing refers to the process of making inferences or educated guesses about a particular parameter. This can either be done using statistics and sample data, or it can be done on the basis of an uncontrolled observational study.

When a predetermined number of subjects in a hypothesis test prove the "alternative hypothesis," then the original hypothesis (the "null hypothesis") is overturned or "rejected." You must decide the level of statistical significance in your hypothesis, as you can never be 100 percent confident in your findings. First, let's examine the steps to test a hypothesis. Then, we'll enjoy some examples of hypothesis testing.

## How to Test a Hypothesis

At this point, you'll already have a hypothesis ready to go. Now, it's time to test your theory. Remember, a hypothesis is a statement regarding what you believe might happen. These are the steps you'll want to take to see if your suppositions stand up:

1. State your null hypothesis. The null hypothesis is a commonly accepted fact. It's the default, or what we'd believe if the experiment was never conducted. It's the least exciting result, showing no significant difference between two or more groups. Researchers work to nullify or disprove null hypotheses.
2. State an alternative hypothesis. You'll want to prove an alternative hypothesis. This is the opposite of the null hypothesis, demonstrating or supporting a statistically significant result. By rejecting the null hypothesis, you accept the alternative hypothesis.
3. Determine a significance level. This is the determiner, also known as the alpha (α). It defines the probability that the null hypothesis will be rejected. A typical significance level is set at 0.05 (or 5%). You may also see 0.1 or 0.01, depending on the area of study.
If you set the alpha at 0.05, then there is a 5% chance you'll find support for the alternative hypothesis (thus rejecting the null hypothesis) when, in truth, the null hypothesis is actually true and you were wrong to reject it.
In other words, the significance level is a statistical way of demonstrating how confident you are in your conclusion. If you set a high alpha (0.25), then you'll have a better shot at supporting your alternative hypothesis, since you don't need to find as big a difference between your test groups. However, you'll also have a bigger chance at being wrong about your conclusion.
4. Calculate the p-value. The p-value, or calculated probability, indicates the probability of achieving the results of the null hypothesis. While the alpha is the significance level you're trying to achieve, the p-level is what your actual data is showing when you calculate it. A low p-value offers stronger support for your alternative hypothesis.
5. Draw a conclusion. If your p-value meets your significance level requirements, then your alternative hypothesis may be valid and you may reject the null hypothesis. In other words, if your p-value is less than your significance level (e.g., if your calculated p-value is 0.02 and your significance level is 0.05), then you can reject the null hypothesis and accept your alternative hypothesis.

## Hypothesis Testing Examples

Let's take those five steps and look at a couple of real-world scenarios.

### Peppermint Essential Oil

Essential oils are becoming more and more popular. Chamomile, lavender, and ylang-ylang are commonly touted as anxiety remedies. Perhaps you'd like to test the healing powers of peppermint essential oil. Your hypothesis might go something like this:

1. Null hypothesis - Peppermint essential oil has no effect on the pangs of anxiety.
2. Alternative hypothesis - Peppermint essential oil alleviates the pangs of anxiety.
3. Significance level - The significance level is 0.25 (allowing for a better shot at proving your alternative hypothesis).
4. P-value - The p-value is calculated as 0.05.
5. Conclusion - After providing one group with peppermint oil and the other with a placebo, you gauge the difference between the two based on self-reported levels of anxiety. Based on your calculations, the difference between the two groups is statistically significant with a p-value of 0.05, well below the defined alpha of 0.25. You conclude that your study supports the alternative hypothesis that peppermint essential oil can alleviate the pangs of anxiety.

### Vitamin C

Is it true that vitamin C has the ability to cure or prevent the common cold? Or is it just a myth? There's nothing like an in-depth experiment to get to the bottom of it all. A potential hypothesis test could look something like this:

1. Null hypothesis - Children who take vitamin C are no less likely to become ill during flu season.
2. Alternative hypothesis - Children who take vitamin C are less likely to become ill during flu season.
3. Significance level - The significance level is 0.05.
4. P-value - The p-value is calculated to be 0.20.
5. Conclusion - After providing one group with vitamin C during flu season and the other with a placebo, you record whether or not participants got sick by the end of flu season. After conducting your statistical analysis on the results, you determine a p-value of 0.20. That is above the desired significance level of 0.05, and thus you fail to reject the null hypothesis. Based on your experiment, there is no support for the (alternative) hypothesis that vitamin C can prevent colds.