Question

How can you use the ANOVA to reject a null hypothesis? How is it related to the F-critical value?

Answer 1

Hint: To answer this question, we first explain what ANOVA is and how we can use this to reject the null hypothesis. ANOVA stands for analysis of variance which is basically a group of different statistical models and its related procedures used to estimate the differences in means. We then explain how we use this to reject a null hypothesis and its relation to the F-critical value.

Complete step by step solution:
ANOVA is a statistical term that stands for Analysis of Variance. It is a group of statistical models and the estimation procedures associated with them. A null hypothesis is basically a statement that specifies that there is no relation between the two measured variables or groups of variables. This hypothesis is key to determine that there is no relation between the two variables and we can test this null hypothesis and come to many useful conclusions. ANOVA test is generally used to compare two means by the use of F-distribution.
We use what is known as the one-way ANOVA which is used to determine the p value from the F value.
Alpha is a value that is used to determine your limit to accept error or in other words, it is used to show the threshold of the user to reject the null hypothesis in spite of it being true. The F value is a value that is calculated from the data set and represents the variance among the set of means. Now, in order to reject the null hypothesis, we need to have an F value greater than the critical value which in terms of p value means that the p value must be less than alpha. Here, p value is the probability of getting an extreme result provided that the null hypothesis is true.
Here, the F-critical value plays a role in rejecting the null hypothesis because if the F-critical value is lower than the F value, we need to reject the null hypothesis.
Hence, under these circumstances only we are to reject the null hypothesis. F-critical value plays a role in this too by helping to decide whether or not to reject the null hypothesis.

Note: It is essential to know the concepts of a null hypothesis and how we are to determine the p value from the F value used in the ANOVA. ANOVA is an extremely important tool used to reject the null hypothesis by providing us the p value and alpha.