A university wants to check if students' choice of major (Science, Arts, or Business) is independent of their gender (Male, Female). A survey is conducted, and the data is summarized in the table below: Major Male Female Total Science 50 40 90 Arts 30 60 90 Business 40 30 70 Total 120 130 250 a) State the null and alternative hypotheses for testing independence. b) Compute the expected frequencies for each cell under the assumption of independence. c) If the Chi-square test statistic is 7.8 and the critical value at 5% significance level is 5.99, what conclusion can be drawn? Instructions Show only the calculations no explanation Show all calculations clearly