What are H0 and Ha for T test

T test:

H0: [x variable] has no relationship with [y variable] when [other x variables] are present in the model.

Ha: [x variable] has a significant relationship with [y variable] when [other x variables] are present in the model.

Note 1: When writing the hypothesis statement you need to replace the terms specified in the square parenthesis with the actual variable names. For instance in the case of Rent, square feet and number of bedrooms example the H0 and Ha for square feet will be stated as follows:

H0: Square feet has no relatoinship with Rent when number of bedrooms is present in the model

Ha: Square feet has a significant relationship with Rent when number of bedrooms is present in the model.

 

Similarly, you can have H0 and Ha for number of bedrooms:

H0: Number of bedrooms has no relationship with Rent when square feet is present in the model

Ha: Number of bedroms has a significant relationship with Rent when square feet is present in the model

Note 2: You need as many H0 / Ha statements as there are number of x varaibles in the model. For instance you have two x variables in the model, then you would need two sets of H0 and Ha, i.e. one set of Ho and Ha for each x variable.

 

Why it is important to say that last phrase “when other x variables are included in the model”?

To explain the answer for this question I will like to show you couple of examples.

First, an analysis where I include just square feet as the x variable to explain Rent (y); and one more separate analysis where I include just number of bedrooms (x variable) to explain Rent (y).

Second, when I include both square feet and number of bedrooms to explain Rent.

Third, when I alter the number of bedrooms slightly and run the analysis again with square feet and number of bedrooms to explain rent (y).