Statistical Inference: Section 4

Question 1

What is the difference between a simple and a composite hypothesis?(1)

Answer 1

Simple tells you everything, composite does not eg for X~N(mu, sigma^2). a hypothesis saying mu=2 and sigma=5 would be simple but just mu=2 and sigma>5 would not be as we arent sure on sigma precisely.

Question 2

What is a type I error?(1)

Answer 2

Reject H0 when it is true.
(usually regarded as more important)
probability of making this error is known as test size (which you want small)

Question 3

What is a type II error?(1)

Answer 3

Accept (fail to reject) H0 when it is false.

Question 4

What is power?(1)

Answer 4

Probability of correctly rejecting the null when it is false. (want high power and small size).

Question 5

How do you calculate signifcance values?(1)

Answer 5

for 2 tailed do 2*(1-pnorm(test statistic))

=p value, obvs less than 0.05 means significant.

Question 6

What is the p-value?(1)

Answer 6

Probability of observing a value as extreme as the one obtained in the experiment if the null hypothesis is true,
It is NOT the probability of the null being true!

Question 7

When is it okay to use binomial proportion assumptions?(1)

Answer 7

When R (sample size) is large, >20, provided pi is less than 95% or greater than 5%.

Question 8

What is the expected value and variance of a binomial random variable?(2)

Answer 8

r*pi (expectation)

rpi)(1-pi