Question

The GMI Rating' 2013 Women on Boards Survey showed that progress on most measures of female board representation continues to be slow. The study reported that 68 of 101 (67%) of French companies sampled, 148 of 212 (70%) of Australian companies sampled, 28 of 30 (93%) of Norwegian companies sampled, 31 of 58 (53%) of Singaporean companies, and 96 of 145 (66%) of Canadian companies sampled have at least one female director on their boards.

a. Is there evidence of a significant difference among the countries with respect to the proportion of companies that have at least one female director on their boards? (USE α = 0.05).

B. Determine the p-value and interpret its meaning

Answer 1

A.

H0: There is no difference among the countries with respect to the proportion of companies that have at least one female director on their boards

H1: There is/are differences among the countries with respect to the proportion of companies that have at least one female director on their boards

For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Degree of freedom = Number of countries - 1 = 5 - 1 = 4

Total number of companies sampled = 101 + 212 + 30 +58 + 145 = 546

Total number of companies with at least one female director on their boards = 68 + 148 + 28 + 31 + 96 = 371

Hypothesized proportion = 371 / 546 = 0.6795

Expected number for French Companies E1 = 101 * 0.6795 = 68.6295

Expected number for Australian Companies E2 = 212 * 0.6795 = 144.054

Expected number for Norwegian Companies E3 = 30 * 0.6795 = 20.385

Expected number for Singaporean Companies E4 = 58 * 0.6795 = 39.411

Expected number for Canadian Companies E5 = 145 * 0.6795 = 98.5275

Chi - square test statistic, =    where Oi and Ei are the observed and expected count.

= (68 - 68.6295)^2 / 68.6295 + (148 - 144.054)^2 / 144.054 + (28 - 20.385)^2 / 20.385 + (31 - 39.411)^2 / 39.411 + (96 - 98.5275)^2 / 98.5275

= 4.818

P-value = P( > 4.818, DF = 4) = 0.3065

As, p-value is greater than the significance level of 0.05, we fail to reject H0 and conclude that there is no statistical significant evidence that there is/are differences among the countries with respect to the proportion of companies that have at least one female director on their boards.

B.

In part A, we have calculated P-value = 0.3065

Interpretation - The probability of finding the observed, or more extreme, results as the one in your sample data, assuming the truth of the null hypothesis (no difference among the countries with respect to the proportion of companies that have at least one female director on their boards) is 0.3065.