9.10 Hypothesis testing of single mean and single proportion:

The hypothesis test itself has an established process. This can be summarized as follows:

1. Determine $H_o$ and $H_a$ . Remember, they are contradictory.
2. Determine the random variable.
3. Determine the distribution for the test.
4. Draw a graph, calculate the test statistic, and use the test statistic to calculate the p-value    . (A z-score and a t-score are examples of test statistics.)
5. Compare the preconceived $\alpha$ with the p-value, make a decision (reject or do not reject $H_o$ ), and write a clear conclusion using English sentences.

Notice that in performing the hypothesis test, you use $\alpha$ and not $\beta$ . $\beta$ is needed to help determine the sample size of the data that is used in calculating the p-value. Rememberthat the quantity $1-\beta$ is called the Power of the Test . A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping $\alpha$ the same. If the power is low, the null hypothesis might not be rejected when it should be.