Question 8 (5 marks) Marks A group of 400 students have had an English test and a Mathematics test. The results of each test are categorised as either bad, average, or good. The following output is obtained using the Pearson's Chi-Squared test in RStudio at a 5% level of significance. Pearson's Chi-squared test X-squared = 20.179, df = 4, p-value = 0.00046 TABLE OF EXPECTED VALUES MathBad MathAverage MathGood EngBad 16.8 52.64 42.56 EngAverage 25.05 78.40 63.46 EngGood 18.25 56.87 45.98 You are to use the above RStudio output and conduct a Chi-square test on independence to test whether the results in English and Mathematics are not independent. a. State the hypothesis statements. [1] b. State any assumptions made. [1] C. State the test statistic including the degrees of freedom. [1] d. Write down the decision clearly stating the reason. [1] e. What is the conclusion? [1]