Hypothesis Testing

Question 1

What is significance?

Answer 1

• α = significance = P(type 1 error)

- When we reject the null hypothesis when it is true

Question 2

What is power?

Answer 2

• β = 1 - power = P(type 2 error)

- Believe the null hypothesis when the alternative is true

Question 3

What is a p-value?

Answer 3

• The probability of getting our test statistic or further away from the middle (more extreme) if the null is true
• Is the area more extreme than our test statistic i.e P-value is P(Z>x)
• Small p-value is evidence against the null hypothesis. For 5% chance of error, we set small to be

Question 4

When do we use the t-dist?

Answer 4

if we don’t know σ

Question 5

What is the t-distibution?

Answer 5

• It is symmetric around 0, mound shaped (like a normal) but has fatter tails
• The higher the degrees of freedom (sample size gets larger), the more normal the curve looks

Question 6

What to do with t-test stat if df is very large?

Answer 6

use Z tables even if σ is unknown

Question 7

What to do with t-test is exact df isn’t available?

Answer 7

If df is not on tables as exact, use whatever df is closest
Difference between values for large df is small

t0.98,114 ≈ t0.95,110 = 1.2893

Question 8

What is true of confidence intervals?

Answer 8

Will always be two tailed

Question 9

What is the hypothesis/confidence relationship?

Answer 9

• Reject = outside confidence itnterval
• Confidence interval is just the acceptance region mapped back to original datas scale
• So if µo lies in the 95% C based on observed data, we would accept Ho in testing µo = µ vs a two-sided alternative at the 5% significance level
• Can use a CI to do a test on a parameter, but are restricted to a particular significance (can’t find p-value)
• If test value of µ is inside confidence interval, know we would not reject the null hypothesis with same significant and 2 tail alternative
• Rejection = not inside CI
• ONLY IF SAME SIGNIFICANCE AND TWO TAILED TEST