Descriptive statistics allow us to describe the distribution of a single variable. This is very useful when needing to know the how one parameter behaves, but it does not provide a definitive answer to questions like:
Is the mean above a certain value?
Is the deviation less than a desired amount?
How do the results for two different groups compare?
Hypothesis testing allows a definitive answer to such questions. A hypothesis tests consists of several elements:
i. null hypothesis
ii. test statistic cut-off (value based on the specified confidence interval)
iii. test statistic sample (value based on the data collected)
iv. decision to “reject the null hypothesis” or to “fail to reject the null hypothesis”
v. explanation of what that result meets in context
Give an example of a hypothesis test. You may choose an example from the textbook, an example from another source, or your own example. Be sure that you provide a citation for any example used.
For your hypothesis test example, identify each of the following:
1) null hypothesis – Explain this null hypothesis. Explain what the alternative hypothesis is. Explain what rejecting the null hypothesis would allow you to conclude.
2a) test statistic utilized – Specify what distribution (z, t, chi-squared, F, etc is considered) is considered.
2b) test statistic cut-off – What is the percent confidence and what value does that give for the border between rejecting and failing to reject the null hypothesis?
2c) test statistic calculated – What value does the test statistic have for the data?
3) decision – Is the calculated test statistic greater than or less than the cut-off value? Do you “reject” or “fail to reject” the null hypothesis?
4) explanation – Explain what this decision means in the context of the problem. Be sure you include the percent confidence and the null/alternative hypothesis in your explanation.
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