TeSts Involving Population Proportions

Question 1

Case I: Test involving one population proportion

H_0:  P  =  P_0
H_1:  P  ≠  P_0
OR
H_1:  P  >  P_0
OR
H_1:  P  <  P_0
Test Statistic Z
Z_calculated  =

Answer 1

(P   - P_0  )/√((P(1-P_0))/n)
Where
  P_0  =   assumed population proportion
  P  =  Observed population proportion  =  x/n
  X   =  number of successes
  n.   =  sample size  

Note: The test statistic for one population proportion and two population proportions is z

Question 2

Tests involving 2 population proportions

Answer 2

Z calculated = (P_1- P_2)/√(P ̅(1- P ̅ )(1/n_1 + 1/n_2 ) )

Where P ̅ = (X_1+ X_2)/(n_2+ n_2 ) = pooled sample proportion
P_1 = x_1/n_1 ; P_2 = x_2/n_2

Question 3

Paired t test
Note: Every condition of the t test applies
Differences:

Answer 3

i. The observations are generated from the same set of respondents, this is not usually the case with independent samples tests
ii. Arising from (i), the two samples often have equal number of observations

Question 4

T calculated is

Answer 4

d-bar all over (standard deviation of d-bar divide by the square root on n). here, d-bar is the mean of the deviations between the two sets of observations, n is the sample size and s-d bar is the standard deviation of the deviations of the observations from the mean of the deviations

Question 5

What does the tank for paired t test look like

Answer 5

X1
X2
D
(D-d bar)
(D-d square)

D= x2-x1

Dbar= mean of d

Sdbar= square root of sum of d-dbar square / n-1