How to Write Hypothesis Test Conclusions (With Examples)
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A hypothesis test conclusion is the outcome of the test, which is based on the results of the test statistic and the value of the critical value. To write a hypothesis test conclusion, it is important to compare the test statistic to the critical value and decide if it is significantly different. If it is, then the null hypothesis is rejected and the alternative hypothesis is accepted. If the test statistic is not significantly different, then the null hypothesis is accepted. Examples of hypothesis test conclusions include “the difference in the means is significant” or “the difference in the means is not significant.”
A is used to test whether or not some hypothesis about a is true.
To perform a hypothesis test in the real world, researchers obtain a from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:
- Null Hypothesis (H 0 ): The sample data occurs purely from chance.
- Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.
If the of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .
Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .
When writing the conclusion of a hypothesis test, we typically include:
- Whether we reject or fail to reject the null hypothesis.
- The significance level.
- A short explanation in the context of the hypothesis test.
For example, we would write:
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…
Or, we would write:
We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…
The following examples show how to write a hypothesis test conclusion in both scenarios.
Example 1: Reject the Null Hypothesis Conclusion
Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
She then performs a hypothesis test at a 5% significance level using the following hypotheses:
- H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
- H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)
Suppose the p-value of the test turns out to be 0.002.
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.
Example 2: Fail to Reject the Null Hypothesis Conclusion
Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.
He performs a hypothesis test at a 10% significance level using the following hypotheses:
- H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
- H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)
Suppose the p-value of the test turns out to be 0.27.
Here is how he would report the results of the hypothesis test:
We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.
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6a.2 - steps for hypothesis tests, the logic of hypothesis testing section .
A hypothesis, in statistics, is a statement about a population parameter, where this statement typically is represented by some specific numerical value. In testing a hypothesis, we use a method where we gather data in an effort to gather evidence about the hypothesis.
How do we decide whether to reject the null hypothesis?
- If the sample data are consistent with the null hypothesis, then we do not reject it.
- If the sample data are inconsistent with the null hypothesis, but consistent with the alternative, then we reject the null hypothesis and conclude that the alternative hypothesis is true.
Six Steps for Hypothesis Tests Section
In hypothesis testing, there are certain steps one must follow. Below these are summarized into six such steps to conducting a test of a hypothesis.
- Set up the hypotheses and check conditions : Each hypothesis test includes two hypotheses about the population. One is the null hypothesis, notated as \(H_0 \), which is a statement of a particular parameter value. This hypothesis is assumed to be true until there is evidence to suggest otherwise. The second hypothesis is called the alternative, or research hypothesis, notated as \(H_a \). The alternative hypothesis is a statement of a range of alternative values in which the parameter may fall. One must also check that any conditions (assumptions) needed to run the test have been satisfied e.g. normality of data, independence, and number of success and failure outcomes.
- Decide on the significance level, \(\alpha \): This value is used as a probability cutoff for making decisions about the null hypothesis. This alpha value represents the probability we are willing to place on our test for making an incorrect decision in regards to rejecting the null hypothesis. The most common \(\alpha \) value is 0.05 or 5%. Other popular choices are 0.01 (1%) and 0.1 (10%).
- Calculate the test statistic: Gather sample data and calculate a test statistic where the sample statistic is compared to the parameter value. The test statistic is calculated under the assumption the null hypothesis is true and incorporates a measure of standard error and assumptions (conditions) related to the sampling distribution.
- Calculate probability value (p-value), or find the rejection region: A p-value is found by using the test statistic to calculate the probability of the sample data producing such a test statistic or one more extreme. The rejection region is found by using alpha to find a critical value; the rejection region is the area that is more extreme than the critical value. We discuss the p-value and rejection region in more detail in the next section.
- Make a decision about the null hypothesis: In this step, we decide to either reject the null hypothesis or decide to fail to reject the null hypothesis. Notice we do not make a decision where we will accept the null hypothesis.
- State an overall conclusion : Once we have found the p-value or rejection region, and made a statistical decision about the null hypothesis (i.e. we will reject the null or fail to reject the null), we then want to summarize our results into an overall conclusion for our test.
We will follow these six steps for the remainder of this Lesson. In the future Lessons, the steps will be followed but may not be explained explicitly.
Step 1 is a very important step to set up correctly. If your hypotheses are incorrect, your conclusion will be incorrect. In this next section, we practice with Step 1 for the one sample situations.
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