The Student Support Department collected data from students registered for IOP2601 in 2023. They wanted to know if there is a difference in the success (performance) in the module between students with a mathematics background and those without a mathematics background. Table 1 provides the performance scores obtained from the 102 randomly selected IOP2601 students. 2 IOP2601/ASSIGNMENT 03/SEMESTER 1/2024 TURN OVER] Table 1 Statistical Data Mathematics background N x s2 With mathematics background 51 5,34 1,28 Without mathematics background 51 4,94 1,29 2.1 Formulate an appropriate null hypothesis (H0) in symbol and in words. (2) 2.2 Formulate an appropriate alternative hypothesis (H1) in symbol and in words. (2) 2.3 Is the hypothesis test in this question one-tailed or two-tailed? (1) 2.4 Assuming that the data are normally distributed, select an appropriate statistical test and calculate the test statistic using the information provided in Table 1. Show ALL calculations. (3) 2.5 Determine the degrees of freedom. (2) 2.6 Using your answers to questions 2.3 and 2.5, determine the critical value for the test for a significance level of 1% (0,01). (1) 2.7 Interpret the results in terms of the rejection or non-rejection of the null hypothesis and justify your answer. (2) 2.8 Interpret your rejection or non-rejection of the null hypothesis in plain language, in terms of the original problem statement. (2)