Top 10 Mistakes of Hypothesis Tests

Summary:  Know your enemy! These are the most common mistakes students make in their hypothesis tests on quizzes. Know the right things to do instead!

Just like Dave’s top ten lists, this list starts with the small things and works up to the great big honkers.

10. Omitting some TI-83/84 inputs

You need to write down enough information when using the stats test menus. This includes the screen name (the whole name, not “PropZTest”), the alternative hypothesis (prop<p_o or μ≠μ_o or whatever), and Pooled when applicable.

If you get a wrong answer, whether you get partial credit depends on what you did. If you leave stuff out, the instructor can’t figure out what you did.

9. Incorrect TI-83/84 inputs

If your H₀ has “25” in it, that’s what you should put for μ_o. If your H₁ or H_a has “≠” in it, that’s what should go in the hypothesis on your TI screen.

8. H₁ contains = or H₀ doesn’t

H₀ comes first and it must contain an = sign. (Some books use ≥, =, and ≤ in H₀.) H_a or H₁ comes second and it must contain >, ≠, or <.

7. Hypothesis missing μ or p or has the wrong one

It’s really not hard if you just think about your data. Numeric data have means μ; binomial data have percents or proportions p.

6. Hypothesis has > or < instead of ≠

If the problem asks you whether something “is” a number or whether two things are “different”, you need to test = and ≠ in your hypotheses. Don’t make assumptions that only > or < matters.

There’s no cool memory trick, because every problem is worded differently. You just need to make it a habit to read each problem carefully and notice whether it’s asking for a two-tailed test (≠) or a one-tailed test (> or <).

Another common problem is misreading “at least” as ≤ instead of the correct ≥, or misreading “no more than” as ≥ instead of the correct ≤. The Symbol Sheet has some common phrases for the inequalities, but again the best practice is just to read the problem carefully and think about what you’re writing.

5. Hypotheses contain sample data

The hypotheses always contain the number that’s part of the claim, never any number from the sample.

Think about it logically! You’re not testing the sample —you know the sample. You’re testing whether something is true about the general population that your sample came from.

4. Using a z test instead of a t test

Be very sure you know the population standard deviation σ before you use a z test. If you don’t know the standard deviation of the population, you can’t use z and you must use t.

Again, no magic bullet here. You need to read the problem carefully.

3. Failing to check for a normal sampling distribution.

Our procedures for testing sample means and proportions require the sampling distribution to be normal, and you’ve learned procedures or rules of thumb to test that. If you don’t make the test, or if the data don’t pass the test, you can’t use a z test or t test.

2. Comparing p to α wrong

I see a lot of papers with α = 0.01 and p = 0.0275, then “p < α”. Everything else is worthless if you get this comparison backward!

Some students write the values of p and α above the symbols, or next to them: “p > α (0.0257 > 0.01)”. That’s perfectly acceptable, and it can help you make the comparisons correctly.

And the #1 mistake of hypothesis testing ...

1. Reaching a conclusion when p > α

When p > α, you fail to reject H₀ (and you don’t even mention H₁). No definite conclusion is possible from this hypothesis test. If H₀ was “the machine is okay” and H₁ was “the machine is broken”, your only possible conclusion is

We can’t tell, at the ____ level of significance, whether the machine is okay or broken.

When p > α you have to write your conclusion in neutral language, not leaning one way or the other.

Don’t say the machine “might” be anything, or “could” be anything. And especially don’t say “we can’t prove it’s broken” or “we can’t prove it’s okay.” Both of those are true, but they’re only half the truth and they lead the reader to a wrong conclusion. (The most effective way to lie is to tell only part of the truth.)

See also:  Proper Conclusions to Your Hypothesis Tests