A Recent Study Measured the Proportion of Business School Faculty

A recent study measured the proportion of business school faculty who engage in outside consulting.Four samples, each composed of 100 randomly selected faculty members, were used to represent four types of institutions: large four-year state schools, small four-year state schools, large four-year private schools, and small four-year private schools.In the sample of 100 faculty from large state schools, 30 reported such outside consulting (30%) , as compared to 24 (24%) in the sample of faculty from small state schools.In the large private school sample, the number was 42 (42%) , as compared to 32 (32%) in the sample of faculty from small private schools. You will use the chi-square distribution to test the hypothesis that the proportion of faculty who engage in outside consulting is the same across all four institutional categories.The p-value for the sample result turns out to be .0522.If the significance level for the test is 1%, what should you conclude?

A) The sample provides strong evidence that the proportion of all state voters who oppose construction of the refinery is the same in all three states.
B) The sample provides strong evidence that the proportion of all state voters who oppose construction of the refinery is not the same in all three states.
C) At a 1% significance level, you can't reject the hypothesis that the proportion of all state voters who oppose construction of the refinery is the same in all three states.
D) At a 1% significance level, you can't accept the hypothesis that the proportion of all state voters who support construction of the refinery is the same in all three states.