Answer to Question #173584 in Statistics and Probability for ANJU JAYACHANDRAN

Question

2. a) There are two samples of 1200 and 900 people drawn from populations respectively,

which have 30% and 25% of fair-haired people. Test whether the samples drawn

from this population maintain difference or not. (Use α = 05.0 )

Answer 1

We have that

n1 = 1200

n2 = 900

p1 = 30% = 0.3

p2 = 25% = 0.25

thus

q1 = 70% = 0.7

q2 = 75% = 0.75

α = 0.05

$$z = \frac{p1 - p2}{\sqrt{\frac{p1q1}{n1}+\frac{p2q2}{n2}}}=\frac{0.3-0.25}{\sqrt{\frac{0.3\cdot0.7}{1200}+\frac{0.25\cdot0.75}{900}}}=\frac{0.05}{0.0195}=2.56$$

Since 2.56 > 1.96 thus Z > 1.96 (at 5% level of significance) we can conclude that it is unlikely that the real difference will be hidden.