# Null hypothesis testing

3b) In this diagnostic, I will set the test a restricted model eliminating the 'smoking', setting this parameter to zero to test against the full regression model. (?)

3c)In this diagnostic, I will set the test a restricted model eliminating the as.factor(race)*ht, setting this parameter to zero to test against the full regression model. (?)

3e) Testing to see if expected birthweight of a child born to a non-white, Non-African American female is the same weight as a child born to an African American mother. In this To do this, I will run a restricted model specifying the race as > 1 to test the races of African American and other on a full regression with all three races. (?)

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#### Solution Preview

I ended up using SAS instead of R. I couldn't get it to start up on my system for some reason. However I copied the dataset from the files So the results should be good.

See attached word document.

Truth tables and conditionals

Consider the truth table for the conditional statement (I will represent the conditional with "ïƒ ")

P Q Pïƒ Q

1. T T T

2. T F F

3. F T T

4. F F T

As we can see from the truth table, the conditional statement, Pïƒ Q is false under one valuation (i.e. assignments of truth values to P, Q) only, and this is when the antecedent is truth and the consequent is false. As such, in all conditional sentences of this type, the conditional will be true when the antecedent is false. To read this off the truth table above simply look at those rows where P, the antecedent of Pïƒ Q is false. You'll note that whenever P is false, Pïƒ Q is true.

So, in answer to your question 1, there are NO cases where a conditional statement is false when the antecedent is false.

An answer to your question 2 follows from this. Consider row 4 ...

#### Solution Summary

The solution answers the question(s) below. The restricted model eliminating for a full regression model is determined.