STATZIKI

Input

Enter proportion 1 (p1)

Enter proportion 2 (p2)

Sample 1 size

Sample 2 size

Formulas and Output

\[H_0:p_1=p_2\] \[H_1:p_1 \neq p_2\] \[P = \frac{n_1\times p_1+n_2\times p_2}{n_1+n_2} = \frac{ 10 \times 0.5 + 2 \times 0.6 }{ 10 + 2 } = 0.51667\] \[Z = \frac{(p_1-p_2)}{\sqrt{P(1-P)(\frac{1}{n_1} +\frac{1}{n_2})}} = \frac{(0.5-0.6)}{\sqrt{ 0.51667 (1- 0.51667 )(\frac{1}{ 10 } +\frac{1}{ 2 })}} = -0.25834\] \[pvalue = 0.39807\]

When should you use two sample proportion test?

Two sample proportion test is used to determine whether the proportions of two groups from different samples differ.
Proportion 1 = n1 / N1
Proportion 2 = n2 / N2

Example, Tim Cook aims to improve the quality of Airpods by reducing defective parts. Therefore, he monitors the efficiency of two assembly lines in the Airpod factory. In line A there are 18 defects reported out of 400 samples. While the line B shows 25 defect out of 350 samples. Is the difference between the two assembly lines significant?

N1 = 400
N2 = 350
Proportion 1 = 18 / 400 = 0.045
Proportion 2 = 25 / 350 = 0.0714