In 2010 91 of households had at least one cell phone A rando

In 2010, 91% of households had at least one cell phone. A random sample of 300 households in each of two different counties indicated the following. At the 0.01 level of significance, can it be concluded that a difference in proportions exists?

Solution

sample proportion for countyX = 255/300 = 0.85 and proportio for county Y = 278/300 = 0.9267......
Let, population proportion for countyX = p1 and population proportion for countyY = p2.....
H0 : p1 =p2 ag. H1: p1 not equals p2.....

pooled mean = p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂) = (0.85+0.9267)*300 / 600 = 0.88835.....

Standard Error = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] } = 0.02571437.....

z = (p₁ - p₂) / Std.Error = ( 0.85 - 0.9267) / 0.02571437 =   -2.982768......

p-value = 0.002856544......which is less than 0.01.....

So, we have to reject H0 and conclude that a difference in proportion exists between the 2 counties!