Consider the Three Approaches to Conducting Hypothesis Tests Under the Maximum

question 17

Multiple Choice

Consider the three approaches to conducting hypothesis tests under the maximum likelihood framework. Which of the following statements are true?
(I) The Wald test is based on estimation only under the null hypothesis
(ii) The likelihood ratio test is based on estimation under both the null and the alternative hypotheses
(iii) The lagrange multiplier test is based on estimation under the alternative hypothesis only
(iv) The usual t and F-tests are examples of Wald tests

• A) (ii) and (iv) only
• B) (i) and (iii) only
• C) (i), (ii), and (iv) only
• D) (i), (ii), (iii), and (iv)

---

Definitions:

Best Fit

A method or line that best approximates the relationship between variables in a set of data.

Minimizes

The process of finding the lowest value of a function, often relevant in optimization problems.

Residuals

The differences between observed and predicted values in a statistical model or analysis.

Actual Y Values

The observed values in a dataset or experiment that are compared against predicted values to assess model accuracy.