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Video Tutorial Summary
Get a quick overview for calculating and interpreting the Z test (to evaluate the Null Hypothesis). The process involves the following five steps:
Look through the given information in the word problem
Calculate the Standard Error
Set the Z critical (one-tail or two-tail; based upon the alpha level)
Calculate the Z test
Decide whether to retain or reject the Null Hypothesis
We reject the null hypothesis when:
The Z test meets or exceeds the Z critical, which indicates that
The p value is .05 or less
Hypothesis Testing begins with the assumption that the null hypothesis is correct. The null hypothesis states that any difference or relationship observed is due to chance. We use the Z test to measure the quality of fit between the sample mean and the Null Hypothesis Distribution. The closer the sample mean is to the null specified mean, the smaller the Z test value.
Retain the Null Hypothesis. A Z test value of 0 indicates that the distribution specified by the null hypothesis is a perfect fit for the sample mean. We'd retain the null hypothesis - no reason to get rid of a null hypothesis that is working just fine.
The Z test tells us the number of standard errors between the sample mean and the null specified population mean. The larger the Z test, the worse the quality of fit between the sample mean and the Null Hypothesis Distribution.
Reject the Null Hypothesis. The researcher typically wishes to show that the null hypothesis is a poor fit for the data, and should be replaced with the research hypothesis. If the Z test is sufficiently extreme (e.g., -1.96 or smaller; +1.96 or larger), then the null hypothesis is rejected in favor of the research hypothesis.
When we reject the null hypothesis, we are supporting the research hypothesis.
Uncertainty. Whenever a decision is based on a sample, there is the possibility that the sample is not representative of the population. We use random selection to eliminate bias, but it does not guarantee us a "perfect sample." If the randomly selected sample is "bad" (i.e., not representative), then the conclusion will be "bad" (i.e., in error). We set alpha to .05, which means that we are willing, 5% of the time, to reject the null hypothesis incorrectly due to a misrepresentative sample. Thus, if the null hypothesis is rejected, we say that we "supported" the research hypothesis, but we would never say that we "proved" the research hypothesis.
To address uncertainty, research is typically replicated. That means we do the research multiple times and see if we consistently get the same or similar results. Sometimes it is a community of researchers working together to replicate a finding and see if it holds over time.
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