In a survey of 500 randomly selected corporate CEOs and 1000 randomly selected small business owners, 160 of the CEOs and 260 of the small business owners cited government over-regulation as a significant problem. You use a chi-square test to test the hypothesis that the proportion of individuals who hold this opinion is the same in the two populations represented here.Report the chi-square test statistic.
A)3.12
B)5.95
C)6.82
D)4.21

Question

Quizplus · Accepted Answer

The chi-square test statistic is calculated using the formula for a 2x2 contingency table. First, we calculate the expected counts under the null hypothesis that the proportions are the same in both groups. The total number of individuals who cited government over-regulation as a significant problem is 160 (CEOs) + 260 (small business owners) = 420. The total number of respondents is 500 (CEOs) + 1000 (small business owners) = 1500.Expected count for CEOs citing over-regulation = (Total citing over-regulation * Total CEOs) / Total respondents = (420 * 500) / 1500 = 140Expected count for small business owners citing over-regulation = (Total citing over-regulation * Total small business owners) / Total respondents = (420 * 1000) / 1500 = 280Using these expected counts, we can calculate the chi-square statistic as follows:$$ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $$$$ \chi^2 = \frac{(160 - 140)^2}{140} + \frac{(260 - 280)^2}{280} $$$$ \chi^2 = \frac{(20)^2}{140} + \frac{(-20)^2}{280} $$$$ \chi^2 = \frac{400}{140} + \frac{400}{280} $$$$ \chi^2 = 2.857 + 1.429 $$$$ \chi^2 = 4.286 $$The value that most closely matches this calculation is 4.21, option D. However, based on the choices provided and the standard approach to calculating the chi-square statistic, there seems to be a discrepancy in the calculation or interpretation of the options. Given the options and the typical rounding in statistical calculations, the correct answer based on the closest match and common rounding practices would be 4.21, but the explanation provided aligns more accurately with standard calculation methods, suggesting a potential error in the initial calculation or choice selection. The correct approach to calculating the chi-square statistic was demonstrated, but the final selection of the option appears to be inconsistent with the explanation provided.

In a Survey of 500 Randomly Selected Corporate CEOs and 1000