9.7:
Decision Making: Traditional Method
The traditional or classical method involves using the critical value to conclude the hypothesis testing.
As a first step, a hypothesis is stated and expressed symbolically as follows.
For the proportion, mean, or standard deviation of a population, the null and alternative hypotheses are expressed as follows.
Further, a critical value is obtained for the chosen parameter in the hypotheses at a specific predetermined significance level α. For proportion, mean, or standard deviation, these critical values at α are the z, t, or chi-square values, respectively, which are calculated using the z, t, or chi-square distributions.
The critical value is then plotted to demarcate the critical region in the probability distribution.
Further, the test statistic is calculated using the sample data and plotted on the probability distribution curve.
The null hypothesis is rejected when the test statistic value falls within the critical region. However, we fail to reject it when the test statistic falls outside the critical region.
9.7:
Decision Making: Traditional Method
The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a neutral statement while the alternative hypothesis can have a direction. The alternative hypothesis can also be the original claim if it involves a specific direction of the parameter.
Once the hypotheses are stated, they are expressed symbolically. As a convention, the null hypothesis would contain the equality symbol, while the alternative hypothesis may contain >, <, or ≠ symbols.
Before proceeding with hypothesis testing, an appropriate significance level must be decided. There is a general convention of choosing a 95% (i.e., 0.95) or 99% (i.e., 0.99) level. Here the α would be 0.05 or 0.01, respectively.
Next, identify an appropriate test statistic. The proportion and mean (when population standard deviation is known) z statistic is preferred. For the mean, when population standard deviation is unknown, it is a t statistic, and for variance (or SD), it is a chi-square statistic.
Then, Calculate the critical value at the given significance level for the test statistic and plot the sampling distribution to observe the critical region. The critical value can be obtained from the z, t, and chi-square tables or electronically using statistical software.
Check if the test statistic falls within the critical region. If it falls within the critical region, reject the null hypothesis.
The decision about the claim about the property of the population or the general interpretation in this method does not require the P-value.