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How Do You Know Which Test to Use?

By calvinw

When you are doing a hypothesis test how do you decide which form to use? Say we are going to test the population proportion .27. Which of the three possibilities do we choose?

\\H_0 :\theta = .27\,\,\,\,\,\,\,\,\,\,\,\,\,\,H_0 :\theta = .27\,\,\,\,\,\,\,\,\,\,\,\,\,\,H_0 :\theta = .27\\H_a :\theta < .27\,\,\,\,\,\,\,\,\,\,\,\,\,\,H_a :\theta > .27\,\,\,\,\,\,\,\,\,\,\,\,\,\,H_a :\theta \ne .27

Part of what makes this hard to figure out is that “the claim” stated in a problem can correspond to either H_a or H_0.You can tell which form to use by the way the question is worded. Let’s look at some typical phrases used with these forms.

If you claim the population proportion “is smaller than 27%” or “is less than 27%” then you would use the form

\\H_0 :\theta = .27 \\H_a :\theta < .27\text{\,\, (your claim) }

and your claim corresponds to the alternative hypothesis.

If you claim the population proportion “is greater than 27%” or “is more than 27%” then you would use the form

\\H_0 :\theta = .27 \\H_a :\theta > .27\text{\,\, (your claim) }

and your claim corresponds to the alternative hypothesis.

If you claim the population proportion “differs from 27%” or “is not equal to 27%” then you would use this form

\\H_0 :\theta = .27 \\H_a :\theta \ne .27 \text{\,\, (your claim) }

and your claim corresponds to the alternative hypothesis.

If you claim the population proportion “is at most 27%” you will use

\\H_0 :\theta = .27\text{\,\, (your claim) } \\H_a :\theta > .27

since the alternative hypothesis to “is at most 27%” would be “is more than 27%”.

If you claim a population proportion “is at least 27%” you will use

\\H_0 :\theta = .27\text{\,\, (your claim) } \\H_a :\theta < .27

since the alternative hypothesis to “is at least 27%” would be “is less than 27%”.

Sometimes these last two cases are written differently by some books. The claim “is at most 27%” is written using the null hypothesis \\H_0 :\theta\leqslant .27 and the claim “is at least 27%” is written with the null hypothesis \\H_0 :\theta\geqslant .27. We’ll stick with our original three forms at the beginning of the post for everything we do though.

This entry was posted on April 26, 2007 at 9:34 pm and is filed under Hypothesis Tests, Module 6 Examples. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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