Statistics 2

Question 1

What is the equation for the product moment correlation coefficient?

Answer 1

r = sxy/square root of (sxx)(syy)

Question 2

What are the conditions for a PMCC?

Answer 2

Population must be bivariate normal
Data from a random sample
Bulk of data should form an ellipse on a scatter diagram

Question 3

Hypothesis test for PMCC

Answer 3

H0:r=0
H1: r>0, r<0, r not equal 0
if r is bigger than or equal to the critical value reject H0

Question 4

Spearman’s rank equation

Answer 4

rs = 1 - 6sumd^2/ n(n^2 -1)

Question 5

Spearman’s hypothesis

Answer 5

H0: no association
H1 : positive association, negative association, some association
If rs is greater than the critical value reject H0

Question 6

What is PMCC?

Answer 6

measures how close to a straight line the points on a scatter graph lie, if r=0 no correlation

Question 7

How do you work out line of regression?

Answer 7

y = a + bx
b = sxy / sxx
a = y bar - b x bar

Question 8

Equation for residuals

Answer 8

observed y value - expected y value
positive - line is too low
negative - line is too high

Question 9

What is interpolation and extrapolation?

Answer 9

Interpolation - reliable- within data set

Extrapolation - out of data range - not reliable

Question 10

Poisson distribution equation

Answer 10

x - p (lamda)

P(X =r) = e^-lamda x lamda^r / r!

Question 11

Conditions for poisson

Answer 11

Random, independent and at a fixed rate of occurrence

mean is roughly equal to the variance

Question 12

Normal distribution

Answer 12

X - N(mean , standard deviation squared)

z = x-mean / standard deviation

Question 13

Normal hypothesis test

Answer 13

H0: mean = k
H1: mean >k, mean
x - N(mean, standard deviation squared/n)
z = sample mean - mean / (standard deviation/square root of n)

Question 14

Estimating variance

Answer 14

n/n-1 [(sum x^2/n) - (sum x/n)^2)]

Question 15

Chi-squared equations

Answer 15

expected = row total x column total/ overall total 
X^2 = (o-e)^2 / e
v = (row-1) (column-1)

Question 16

Chi-squared hypothesis

Answer 16

H0: no association
H1: some association
X^2 is greater than the critical value, reject H0

Question 17

Approximating

Binomial to poisson

Answer 17

X - B(n,p) —————–> X - P(np)
n is large
p is small

Question 18

Approximating

Poisson to normal

Answer 18

X - P(lamda) ————–> X - N(lamda, lamda)
lamda is bigger than 10
continuity correction

Question 19

Approximating

Binomial to normal

Answer 19

X - B(n,p) ————> X - N(np, npq)
n is large
p is roughly 1/2

Question 20

What is a continuity correction?

Answer 20

make the equal to group 0.5 bigger

Question 21

What is the assumption for chi squared?

Answer 21

Independent