QA6 - Hypothesis Testing

Question 1

Explain the difference between Type I and Type II errors and how these relate to the size and power of a test

Answer 1

Type I is rejecting a true null hypothesis, probability is the size and denoted alpha

Type II error is not rejecting null hypothesis when alternative is true, denoted (1 - beta) and is the power of a test

Question 2

Understand how a hypothesis test and a confidence interval are related

Answer 2

Confidence interval will contain the null hypothesis if not rejected

Question 3

Explain what the p-value of a hypothesis test

Answer 3

Probability of observing a test statistic more extreme than computed when the null is true

Question 4

Construct and apply confidence intervals for one-sided and two-sided hypothesis tests and interpret the results of hypothesis tests with a specific confidence level

Answer 4

two: [mu_hat +/- C(alpha/2) * sigma_hat / sqrt(n)]
one: [mu_hat - C(alpha/2) * sigma_hat / sqrt(n), infinity)
(-infinity, mu_hat + C(alpha/2) * sigma_hat / sqrt(n)]

Question 5

Identify the steps to test a hypothesis about the difference of two population means

Answer 5

H0: mu1 - mu2= 0