07 Normal Distribution: Hypothesis Testing

Question 1

What are the five steps in Hypothesis testing?

Answer 1

1) Formulate the hypothesis
2) Find likelihood ratio test statistic & distribution
3) Calculate empirical value of the test statistic
4) Determine H₀ rejection region & decide about test outcome (at significance level α)
5) Interpret results

Question 2

What is Ω₀?

Answer 2

1) sample space Ω is the set of all possible outcomes.
2) Ω₀ is called “omega zero space”
3) Ω₀ is a null set or reduced model

Question 3

Which assumption determines your formulas when conducting a likelihood ratio test?

Answer 3

Whether Σ is known or unknown.

Question 4

What is the likelihood ratio test?

Answer 4

A likelihood-ratio test (LR test) is used for comparing the goodness of fit of two statistical models—a null model (representing the null hypothesis) against an alternative model (representing an alternative hypothesis).

Question 5

How do you decide whether to reject the null hypothesis in hypothesis testing?

Answer 5

1) you determine the rejection region

2) you decide about the test outcome given the significance level alpha

Question 6

What is a pooled covariance matrix?

Answer 6

When comparing means of two different samples, the pooled covariance matrix combines the information from the two samples into one estimated population covariance.
See also:
Assuming equal population variances, the pooled sample variance provides a higher precision estimate than the individual sample variances -> can lead to increased statistical power in statistical tests that compare the populations

Question 7

What do you need in order to calculate the confidence interval?

Answer 7

• x̅ = the empirical means
• sⱼⱼ = the empirical var-cov matrix
• p, n & α to get the F-test statistic

Question 8

Which assumption determines your formulas when comparing vectors of means in hypothesis testing?

Answer 8

Whether the covariance matrices are equal = whether Σ₁ = Σ₂ = … = Σₚ or Σ₁ ≠ Σ₂