Answer to Question #153774 in Statistics and Probability for vishnu

Question #153774

In a sample of 500 persons from Town A, 200 are found to be consumers of Wheat. In a sample of 400 from Town B, 220 are found to be consumers of Wheat. Do these data reveal a significant difference between Town A and Town B as far as the proportion of Wheat consumers is concerned?

Expert's answer

H₀: Two towns do not differ much as far as the proportion of wheat consumption. P₁ = P₂

H1: P₁ ≠ P₂

The Statistic test is

"Z = \\frac{p_1-p_2}{\\sqrt{PQ(\\frac{1}{n_1}+ \\frac{1}{n_2})}} \\\\\n\np_1 = \\frac{200}{500} =0.4 \\\\\n\np_2 = \\frac{220}{400} = 0.55 \\\\\n\nP = \\frac{n_1p_1+n_2p_2}{n_1+n_2} \\\\\n\n= \\frac{500(0.4) + 400(0.55)}{500+400} \\\\\n\n= \\frac{200+220}{900} \\\\\n\n= 0.466 \\\\\n\nQ = 1 -P = 1 -0.466 = 0.534 \\\\\n\nZ = \\frac{0.4-0.55}{\\sqrt{(0.466)(0.534)(\\frac{1}{500}+ \\frac{1}{400})}} \\\\\n\n= \\frac{0.15}{0.03346} \\\\\n\n= 4.48"

Calculated value Z = 4.48

Tabulated value of Z at 5% level of significance for a two tail test is 1.96

Calculated value >Tabulated value, H₀ is rejected.

Hence the data reveal a significant difference between town A and town B so far as the proportion of wheat consumers is concerned.