Statistics Lecture 8.3: Hypothesis Testing for Population Proportion. Testing a Claim about a Population Proportion.
State the null hypothesis and the alternative hypothesis. The null hypothesis (H0) always contains an equality, and is the one you are trying to refute. The alternative (research) hypothesis never contains an equality, and is the one you are trying to confirm. These two hypotheses are stated so that they are mutually exclusive and collectively exhaustive. Mutually exclusive means that if one is true, the other must be false, and vice versa. Collectively exhaustive means that at least one of the outcomes must occur. Your hypotheses are formulated depending on whether it is right-tailed, left-tailed, or 2-tailed:
- Right-tailed: Research question: Is the sample proportion greater than the hypothesized population proportion? Your hypotheses would be stated as follows: H0: p<=p0; Ha: p>p0.
- Left-tailed: Research question: Is the sample proportion less than the hypothesized population proportion? Your hypotheses would be stated as follows: H0: p>=p0; Ha: p<p0.
- Two-tailed: Research question: Is the sample proportion different from the hypothesized population proportion? Your hypotheses would be stated as follows: H0: p=p0; Ha: p<>p0.
- In your example, you can use a two-tailed test to see if the sample proportion of male births, 0.53, is different from the hypothesized population proportion of 0.50. So H0: p=0.50; Ha: p<>0.50. Typically, if there is no a priori reason to believe that any differences must be unidirectional, the two-tailed test is preferred as it is a more stringent test.