Stats A level

Question 1

random

Answer 1

• generate random numbers - calculator or out of a hat

Adv: completely unbiased
Dis: inconvenient if population spread over large area

Question 2

systematic

Answer 2

• give number to each population member and calculate a regular interval to use by dividing population by sample size
• generate random starting point (less than or equal to interval) and then keep adding interval

Adv: should give unbiased
Dis: issue of patterns

Question 3

Stratified

Answer 3

• if population is divided into categories, use same proportion of each category in sample as there is in population

Adv: representative
Dis: expensive, not useful if no obvious categories

Question 4

Quota

Answer 4

• divide population into categories and give each a quota
  Adv: useful if whole population not available, still possible as just pick people who are
  Dis: easily biased by interviewer

Question 5

when will an iteration converge?

Answer 5

if x0 close enough to the root
f’(x) between -1 and 1

Question 6

when will newton raphson not work

Answer 6

• tangent very shallow gradient/ f’(x)=0 - if it is a straight line and so will never reach x axis

Question 7

when will trapezium rule under/over estimate

Answer 7

under = concave
over = convex

Question 8

conditions for binomial distribution

Answer 8

fixed number (n) trials
success/failure
independent events
same probabilityn

Question 9

normal distribution

Answer 9

68% - one standard deviation of mean
95% - 2 standard deviation away from mean
99.7% - 3 standard deviations

inflection = mean + standard deviation

Question 10

when to approximate normal to binomial

Answer 10

p close to 0.5 and n is large
np and n(1-p) >5