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Structure of a Hypothesis Test
The following should be included in all hypothesis tests:
1. A statement of competing hypotheses ( vs. )
2. A decision rule for rejecting (based on )
3. A decision criterion rule (the physical value of the random variable that represents the
required “extremeness” of our observed sample value.
4. A conclusion statement (what the sample data tells you to conclude)
As an important note: we never say, “accept as true.” Instead, we remain accurate and say
that there is simply not enough evidence to reject it. Think about this as “innocent,” vs. “not
guilty.” Just because a court cannot prove that someone is guilty, they don‟t say that he is
innocent. Instead, they give the verdict of “not guilty.”
Homework Problems – 7.1
1. In your own words, explain the difference between the null and alternative hypotheses.
Also, explain how to identify each in a research study.
2. Explain why we assume that the null hypothesis is true before testing a hypothesis.
3. It is believed that 7% ( ) of an organic corn crop is lost to insect infestations. An
organic farmer has devised a system that may result in less insect destruction. He would
like to test this idea with a hypothesis test. Write the competing hypotheses.
4. A high school statistics class typically gets an average of scores out of 5 on an
Advanced Placement (AP) exam. Over the recent several years, he has found that his
students‟ scores were higher. He would like to test this hypothesis. Write the competing
hypotheses.
5. A snack dispenser has a failure rate of over a 5-year span. After changes to the
machine, the manufacturer would like to know whether or not this has changed. Write
competing hypotheses.
6. What does it mean to say that when describing a Type I error
7. Based on the “Structure of a Hypothesis Test” blue box, fully describe the hypothesis test
for the scenario in question 3, assuming and that he finds that only 52 out of
1000 bushels of his crop are lost to insect infestations.
8. Based on the “Structure of a Hypothesis Test” blue box, fully describe the hypothesis test
for the scenario in question 4, assuming and that he finds his students have
been averaging ̅ on the test.
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