Last Minute

Question 1

What probability formula is used for marginal and joint probability tables

Answer 1

P(A|B) = P(A n B) / P(B)

Question 2

What is a marginal and joint probability table

Answer 2

A table showing the probabilites for all combinations of 4 different variables and the probability for the totals

Question 3

What can be used when working out n amount chosen from r

Answer 3

nCr

Question 4

What is Bayes Rule

Answer 4

P(A|B) = P(B|A) * P(A) / P(B)

Question 5

What is the formula for binomial

Answer 5

• P(X = k)
• (n! / k! * (n-k)!) * p^k * q^n-k

Question 6

What is the formula for the poisson

Answer 6

• P(X = k) = e^-lambda * lambda^k / k!

Question 7

What is the z test statistic for hypothesis testing (population)

Answer 7

z = x bar - mu / sigma / root(n)

Question 8

what is the t test statistic for hypothesis testing (sample)

Answer 8

t = x bar - mu / s / root n

Question 9

What is the formula for Bias

Answer 9

• Bias(theta hat) = E(theta hat) - theta

Question 10

When is one estimator said to be more efficient than the other

Answer 10

• Var(theta 1 hat) < Var(theta 2 hat) then theta 1 hat is more efficient
• whichever one is less

Question 11

How is the relative efficency of two estimators calculated

Answer 11

• With respect to is key
• whichever estimator it is in respect to, this estimator is on top
• Var(theta 1 hat) / Var(theta 2 hat)

Question 12

What is the mean of the sampling distribution s^2

Answer 12

• σ^2

Question 13

What is the formula for the chi squared test statsitc

Answer 13

chi square = (n-1) * s^2 / σ^2

Question 14

How is the t value calculated for testing if a coefficient is significant in regression

Answer 14

• t = coefficient / standard error

Question 15

What is the formula for the exponential distribution

Answer 15

• f(t) = lambda * e^-lambda * t

Question 16

When would a finite population coefficient be used

Answer 16

• When n is not a small fraction of N
• N - n / n - 1
• applied to variance

Question 17

How is TSS calculated

Answer 17

• TSS = RSS + ESS

Question 18

What is key about RSS

Answer 18

• It is the explained variation in variable A by variable B

Question 19

How is the coefficient of determination calculated

Answer 19

• R^2 = RSS / TSS

Question 20

What is the hypothesis for a coefficient significance test

Answer 20

• H0: Hypothesised slope = 0
• H1: Hypothesised slope /= 0

Question 21

How is the F-test and t-test related

Answer 21

• F = t^2

Question 22

What is the formula for an overall test of significance

Answer 22

• F = (RSS / k) / (ESS / n-K-1)
• Reject H0 if F > F(k numerator degrees, n-k-1 denomiator degrees, aplha)

Question 23

What is the hypothesis for overall significance

Answer 23

H0: All coefficients = 0
H1: at least one coefficient is not 0

Question 24

What is the F statisitc for a subset of coefficients

Answer 24

• F = ((ESS(r) - ESS) / r) / (ESS / n-k-r-1)
• r is the number of excluded variables