Proportion of wheat consumed?


#1

In a random sample of 1000 persons from town A,400 are found to be consumers of wheat.in a sample of 800 from town B,400 are found to be consumers of wheat.Do these data reveal a significant difference between town A and town B,so far as the proportion of wheat consumed is concerned?


#2

let us set up the hypothesis that the two towns do not differ so far as proportion of wheat consumers is concerned, i.e. H0 : p1 = p2 against Ha : p1 ≠ p2.
Computing the standard error of the difference of proportions:

n1 = 1000, p1 = 400/1000 = 0.4; n2 = 800; p2 = 400/800 = 0.5

p = (1000 × 0.4) + (800 × 0.5)/(1000 + 800) = 400 + 400/1800

simply p = (x1 + x2)/(n1 + n2) = (400 + 400)/(1000 + 800)/1800 = 4/9

q = 1 –(4/9) = 5/9

p1 – p2 = 0.4 – 0.5 = -0.1

difference/S.E. = 0.1/0.024 = 4.17.

Since the difference is more than 2.58 S.E. (1% level of significance). It could not have arisen due to fluctuations of sampling. Hence the data reveal a significant difference between town A and town B so far as the proportion of wheat consumers is concerned