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Summary statistical distributions and formula's

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Comprehensive A-level statistics notes, featuring clear explanations, practical examples, key formulas, visual aids, and concise summaries of essential concepts.

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  • July 26, 2024
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Statistical distributions

Binomial PD when P x x

Binomial CD when P x 4 x



Cumulative probabilities


Phrase means calculation

i n
ooo no more than 3 X E 3 P OC I 3

X 27 X 7 1

o o fewer than 10 X L 10 P X I 10 1

at most g y g g P X E 8




greater than equal to
less than l y se I



Igreater than
I less than equal to


Hypothesis testing
ins of winning
Badluck but the game is not rigged 17 0.2


P 0.21
Ho the null hypothesis the that we assume to be true
Hq the alternative hypothesis thing
what we think could be given our
observed data IP20.21

, I



X the test statistic the that we are observing
thing

a write down a suitable test statistic
let X be the number of people who support the candidate

b write down two suitable hypothesis
Ho i P 0.4
H P 20.4

C explain the condition under which the null hypothesis would be
rejected
If PIX I 3 L 0.05 then we would reject Ho Accept H

al let be the number of late students
b Ho P 0.05
H p 0.05 significance level
c if pix I then we would reject Ho Accept H
Assi'ming
t true x 13140,0 051
P 261 I PIX 51
I 0.9861
0 0139 L O 1

we
problem
reject Ho meaning
with lateness
the school has a



Hypothesis tests with alternative hypotheses in the form trips
and Hi p are called one tailed tests

Hypothesis tests with an alternative hypothesis in the form to p
are called two tailed tests

Critical values and critical regions
A prize is given out 1 in 5 plays
The game is played 40 times i I expect to win 8 times on averas
what observed data would make me suspicious that the game
was giving out a prize
significance level of 5

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