Exam Preparation

Question 1

var(X)

Answer 1

= E(X²) – E(X)²

Question 2

E(Y|X)

Answer 2

= X × E(Y)

Question 3

Variance using LIE

Answer 3

1. w × var(A) + w × var(B)
2. w × (E(A) – E(Total))² + w × (E(B) – E(Total))²
3. Add (1) and (2)

Question 4

Sample mean for more than two outcomes

Answer 4

Can do it but need two define variables - eg. as ‘1’ or ‘0’

Question 5

Sampling Distribution

Answer 5

The probability distribution of a sample statistic over all possible samples from the population

Question 6

Sample Mean is unbiased when

Answer 6

• Expected value of sampling distribution is equal to the population mean
• Can exist when n=1
• May not be true when the sample is not representative of the population

Question 7

Larger Sample Size

Answer 7

• Reduces the variance of x̄
• Makes no difference to the bias of x̄

Question 8

Standard Error of Difference
se(x̄1 – x̄2)

Answer 8

√(se(x̄1)² + se(x̄2)²)

Question 9

Variance of Weighted Functions

On Formula Sheet

Answer 9

var(a + bZ) = b² × var(Z)

Question 10

T Statistic

Answer 10

t = (x̄ - μ) / s.e

Question 11

S.E for T Statistic

Answer 11

σ / √n

Question 12

T Statistic for Difference of Two Means: Independent Samples

Answer 12

t = (x̄1 – x̄2) / s.e.(x̄1 – x̄2)

Question 13

Consistent Sample

Answer 13

• Variance changes with the sample size
• Unbiased

Question 14

Independent Samples

Answer 14

Each individual has equal chance to be chosen.

Therefore, independent surveys have a change of including the same person across them.

Question 15

T Values for Regression

Answer 15

t = β1 / s.e(β1) or t = β0 / s.e(β0)

Question 16

Su

Answer 16

=√(Sum of Squared Residuals/(n-2))

or =√(Sum of Squared Errors/(n-2))

Question 17

R²

Answer 17

=var(Ŷ)/var(Y)

Question 18

Ŷ

Answer 18

β0 + (β1 × X)

Question 19

Type I and Type II Errors

Answer 19

+——–| True ——| False —-|
+——–+————–+————+
Accept | No error | Type II
+——–+————–+————+
Reject | Type I | No error |

Question 20

Variance for Bernoulli Distribution

Answer 20

Var = p(1 – p)

Question 21

Interpreting β1

Answer 21

1% increase is associated with a x% increase in…

Question 22

Interpreting R²

Answer 22

The % that y is explained by x

Question 23

Confidence Interval for T Statistic

Answer 23

[x̄±t(α/n,n-1) × s.e.(x̄)]

Question 24

Confidence Interval for Independent Samples

Answer 24

[(x̄1– x̄2)±t(α/2,n1+n2 – 2) × s.e.(x̄1– x̄2)]

Question 25

Confidence Interval for Regression

Answer 25

β̂1± t(α/2,df) × s.e.(β̂1)

Question 26

Variance of T Distribution

Answer 26

v/v–2

Question 27

Probability of a Type I Error

Answer 27

Significance level %

Question 28

Power

Answer 28

Probability of not making a type II error

Question 29

Standard Error for Proportions only

Answer 29

√(p̂(1 – p̂)/n)

Question 30

T Statistic for Proportions

Answer 30

(p̂ – p)/se(p̂)

Question 31

T Statistic for Difference of Two Means: Matched Pairs

Answer 31

tn-1 = (d̄)/(sd/√n)

Question 32

d̄

Answer 32

x̄1– x̄2

Question 33

Degrees of Freedom for Regression

Answer 33

Minus two for beta1 and beta0