Z-Test (Z₀, Z_e & H₀) for p₁ = 0.65 & p₂ = 0.72 with P Values 0.34 & 0.39

Workout :
step 1 Address the formula input parameters and values
Sample Proportion p₁ = 0.65
Sample Proportion p₂ = 0.72
Population Probability P₁ = 0.34
Population Probability P₂ = 0.39
Sample Size n₁ = 89
Sample Size n₂ = 95
z score value (z) = 0.7
Formula
Z₀=p₁ - p₂
√

((P₁Q₁) / n₁ + (P₁Q₁) / n₂)

step 2 Find Q₁ and Q₂ from P₁ and P₂ respectively
Q₁ = 1 - P₁
Q₁ = 0.66
Q₂ = 1 - P₂
Q₂ = 0.61

step 3 Substitute p₁, p₂, P₁, P₂, Q₁, Q₂, n₁ & n₂ value in the below formula for test of significance for difference between two proportion having known P₁ & P₂ values.
=0.65 - 0.72
√

{(0.34 x 0.66) / 89} + {(0.39 x 0.61) / 95}

step 4 Simplify the above expression
=0.07
√

{(0.34 x 0.66) / 89} + {(0.39 x 0.61) / 95}

=0.07
√

(0.2244 / 89) + (0.2379/95)

=0.07
√

0.0025213483146067 + 0.0025042105263158

=0.07
√

0.0050255588409225

=0.070.0709

Z₀ = 0.9874

Inference
There is significance difference
since the calculated value of Z₀ = 0.9874 is greater than the table value of Z_e = 0.7.
Therefore the null hypothesis H₀ is rejected.