Chapter 20. Testing Hypotheses about Proportions. Hypothesis Testing: used to assess the evidence provided by data in favor of some claim about the population. We are trying to prove something (H a ) has changed compared to what it was before (H o ). H a can be one sided or two sided.
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Testing Hypotheses about Proportions
If Ha is one sided, then we test to see if the true proportion is either larger or smaller than the claim. . This is also referred to as a one-tailed test.
If Ha is two sided, then we test to see if the true proportion is different than the claim. This is also referred to as a two-tailed test.
1) State Ho and Ha.
2) Specify significance level, .
3) Identify correct test and conditions.
4) Calculate the value of the test statistic
5) Find the P-value for the observed data
(If the P-value is less than or = to , the test
result is “statistically significant at level .)
6) Answer the question in context.
statistic – parameter______
standard deviation of statistic
(look familiar? It should, it’s just z!)
Test Statistic for a proportion:
Ho: p = po (the pop. proportion is the true center)
and one of the following:
Ha : p > po (seeks evidence that the pop. prop is larger)
Ha: p < po (seeks evidence that the pop. prop is smaller)
Ha: p po (seeks evidence that the pop. prop is different)
(po is replaced with a numerical value of interest)
You can reject the null hypothesis, but you can never “accept” or “prove” the null.
(Proving the null was never your intention. We take for granted it is true from the start but we never prove it.)