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
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
