A2 Stats

Question 1

describe exponential modelling

Answer 1

use logs & coding to convert exponential relationship to linear relationship & use regression line
y = ax^n –> logy = nlogx + loga & plot logx against logy

y=kb^x
logy = xlogb + logk & plot x against logy

Question 2

define PMCC

Answer 2

product moment correlation coefficient
numerical measure of the type & strength of linear correlation

Question 3

what is the PMCC for a sample & population represented by?

Answer 3

for sample: r
for population: ρ

Question 4

what values is r b/w?

Answer 4

-1 ≤ r ≤ 1
r = 1 linear & positive correlation
r = -1 linear & negative correlation
r = 0 no correlation

Question 5

what does n/a mean in table?

Answer 5

data for that day is not available
remove the points from calculations

Question 6

describe how to find PMCC using calculator

Answer 6

menu –> 6: statistics
2: y = a + bx
enter values for x & y
option –> 4: regression calc
PMCC is r value

Question 7

comment on suitability of a linear regression or exponential model for given data

Answer 7

e.g. as r is very close to 1, there is strong positive correlation b/w ___________. therefore the data points lie close to a straight line so a linear regression model is suitable for __________ data
so exponential model is suitable for raw data

Question 8

what constitutes a ‘strong correlation’?

Answer 8

generally over 0.6 or less than -0.6

Question 9

describe how to find equation of the regression line from coded data

Answer 9

‘unlog’
compare with the equation y = mx + c
logb =
loga =
work out a & b
state the equation at the end

Question 10

what does significance level mean?

Answer 10

the chance of incorrectly rejecting H0 when it is true

Question 11

what must the conclusion of a hypothesis test include?

Answer 11

accept/reject H0
RELATE TO CONTEXT OF THE Q

Question 12

what is PMCC hypothesis testing used for?

Answer 12

used to determine whether the PMCC for a sample, r, indicates that there is likely to be a linear relationship within the population

Question 13

what are the null & alternative hypotheses for PMCC hypothesis testing?

Answer 13

the H0 is always that there is no correlation in the population ρ = 0

for positive correlation ρ > 0
for negative correlation ρ < 0
for any correlation ρ ≠ 0 (NB halve the significance level)

Question 14

describe the method of a PMCC hypothesis test

Answer 14

1. state H0: ρ = 0
   & H1
2. significance level =
3. n =
   (n is number of pairs of data)
4. find critical value using the PMCC table in data booklet (one +ve & one -ve for 2-tailed test)
5. do number line & if r value is outside critical region (see OneNote) then accept H0, but if r value is inside the critical region, reject H0
6. conclusion
   e.g. as 0.1149 (r-value) < 0.5067 (critical value), it is not in the critical region so we accept H0. there is not sufficient evidence of a positive correlation b/w daily maximum gust & relative humidity (linking to Q)

Question 15

for any set notation Q, what is the first step?

Answer 15

draw Venn Diagram

Question 16

dot method for P(A’ u B’) or P(A’ u B’)

Answer 16

for u: add things with at least 1 dot
for n: add things with all the dots

Question 17

describe conditional probability

Answer 17

the probability of an event can change depending on the outcome of a previous event
the probability that event B occurs, GIVEN that event A has already occured

Question 18

what is the notation for conditional probability?

Answer 18

P(B|A)
the probability that event B occurs, GIVEN that event A has already occured

Question 19

usually P(B|A)…

Answer 19

≠ P(A|B)

Question 20

in conditional probability, if A & B are independent, what is the formula?

Answer 20

P(B|A) = P(B|A’) = P(B)

Question 21

two-way table

Answer 21

see OneNote & notes in folder
write down marginal totals

Question 23

what is the addition formula?

Answer 23

P(A u B) = P(A) + P(B) - P(A n B)

Question 24

what is the multiplication formula?