Final answer:
To make valid inferences in hypothesis testing, one must understand steps from stating hypotheses to calculating the test statistic and p-value, and finally making a decision regarding the null hypothesis. We never prove a hypothesis, but provide evidence against the null hypothesis based on probability.
Step-by-step explanation:
In order to make valid inferences and correctly perform hypothesis testing, it is essential to understand the entire process which includes several steps. First, a null hypothesis (typically symbolized as H0) and an alternative hypothesis (H1 or Ha) must be stated. The null hypothesis often represents a statement of 'no effect' or 'no difference' and is what you are trying to find evidence against through your sample data.
The random variable (P') is then defined as a quantity whose variation is random and which is observed in the phenomena being studied. After defining the random variable, the test statistic is calculated, which provides the basis for deciding whether to reject the H0. This statistic is compared against a distribution to find the p-value, the probability of observing the data if the null hypothesis is true.
If the p-value is less than the chosen significance level, here mentioned as the 5 percent level, then the null hypothesis is rejected, which leads to supporting the alternative hypothesis. Rejecting H0 when it is true constitutes a Type I error, while not rejecting H0 when it is false is known as a Type II error.
An essential part of hypothesis testing is understanding that we can never say a hypothesis is proven true or false with absolute certainty; rather, we provide evidence against the null hypothesis based on the likelihood of a sample statistic if the null hypothesis were true.