Answer to Question #144992 in Statistics and Probability for d

Question

The result of a certain survey shows that out of 50 ordinary shops of
small size, 35 are managed by men of which 17 are in cities. 12 shops in
villages are run by women. Can it be inferred that shops run by women
are relatively more in villages than in cities ? Use chi-square test. ( Table
value of chi-square for one degree of freedom at 5% level is 3.841.

Answer 1

The following information is obtained concerning an investigation of 50 ordinary shops of small size:

Take the hypothesis that there is no difference so far as shops run by men and women in towns and villages. With this hypothesis the expectation of shops run by men in towns would be:

Expectation of (AB ) = $\frac{A * B}{N}$

where A = shops run by men,(A) = 35, B = shops in towns,; (B) = 20 and N = 50

Thus, expectation of (AB) = $\frac{35*20}{50}$ =14

Hence, table of expected frequencies would be:

$\tilde{\chi}^2=\sum_{k=1}^{n} \frac{(O_k - E_k)^2}{E_k}$ =3.57

Given critical value = 3.841. The calculated value of χ2 is less than its table value. Hence the hypothesis stands. We can conclude that there is no difference between shops run by men and women in villages and towns.