Final answer:
In order to determine the necessary sample size, a researcher using an alpha of .01 and a power of .80 must know the expected effect size, which helps in calculating the sufficient sample size for detecting the intended effect with the specified power.
Step-by-step explanation:
To determine the sample size needed when a researcher decides to use an alpha of .01 and a power of .80, the researcher must ascertain the expected effect size. The effect size is a measure of the magnitude of the difference that is being tested for, such as the difference between two means or proportions. Knowing the effect size facilitates calculation of the necessary sample size to achieve the desired power for the test.
The alpha value indicates the significance level, which is the probability of rejecting the null hypothesis when it is actually true (a Type I error). A lower alpha value like .01 means that the researcher is allowing for a very low probability of falsely detecting an effect. The power of a test, 1-β, where β is the probability of a Type II error, represents the likelihood that the test will correctly reject a false null hypothesis. A power of .80 suggests that the researcher wants a 80% chance of correctly detecting an effect, should one actually exist.
For example, if we consider the statement that 'at the 1 percent significance level, there is not enough evidence to conclude that freshmen students study less than 2.5 hours per day, on average,' the alpha being referenced is the cutoff for determining whether there is significant evidence to reject the null hypothesis. A power analysis would use this alpha along with the desired power and the estimated effect size to determine the minimum sample size needed.