statistics year 1

Question 1

mutually exclusive

Answer 1

• if events are mutually exclusive it means they cannot happen in the same trial
  P(A or B)= P(A) + P(B)

Question 2

complementary events

Answer 2

• when something is mutually exclusive and exhaustive
  eg two events A and not A
  P(A’)= 1- P(A)

Question 3

independent events

Answer 3

when one event doesnt affect the probability of another event occurring
P(A and B)= P(A) x P(B)

Question 4

probability distribution function

Answer 4

• function that gives the probabilities of all possible outcomes of an experiment. A discrete random variable X takes values x with probabilities P(X=x)

Question 5

conditions for a binomial probability distribution

Answer 5

• two possible outcomes in each trial
• fixed number of trials
• independent trials
• identical trials (p is the same for each trial)

Question 6

critical region

Answer 6

set of values that leads you to reject the null hypothesis

Question 7

acceptance region

Answer 7

set of values that leads you to accept the null hypothesis

Question 8

critical value

Answer 8

lies on the border of the critical region. Depends on the significance level of the test. The critical region includes the critical value and all values that are more extreme than that

Question 9

significance level

Answer 9

every hypothesis test has a significance level. This is equal to the probability of incorrectly rejecting the null hypothesis
- if you use a low significance level eg 1% then you can be fairly certain of your result if you reject the null hypothesis. If you reject the null hypothesis using a high significance level eg 20% then you may need to carry out further tests to be sure of your result
after carrying out a hypothesis test you must state whether you accept or reject the null hypothesis and must also state a conclusion that relates directly to the problem

Question 10

what happens as you lower the significance level

Answer 10

you need more evidence to reject the null hypothesis and you lower the chance of making an incorrect conclusion