IOP2601 Assignment 3 Semester 2 Due 23 September 2024

UESTION 1 [5] 1.1 Indicate whether the following statements are True or False. a) A non-directional hypothesis is used when there is no prior theoretical basis for predicting the specific direction of the effect or relationship between variables. (1) b) In a study testing a directional hypothesis, the critical region for rejecting the null hypothesis is split into two tails of the distribution. (1) c) A non-directional hypothesis always predicts that there will be no difference or relationship between variables. (1) 1.2 A researcher is investigating the effectiveness of a new teaching method in improving students’ test scores relative to a traditional teaching method. The researcher anticipates that the new method will result in significantly higher test scores based on prior research findings. Based on this context, formulate a directional hypothesis. (2) QUESTION 2 [15] A researcher is investigating whether South African high school students who use the new digital learning platform achieve higher academic performance compared to those who receive the traditional classroom instruction. Prior research indicates that the digital learning platform is expected to result in higher academic performance scores. Table 1 provides the scores obtained from 100 randomly selected students. Table 1 Academic Performance Scores N x̅s2 Digital Learning Platform (DLP) 31 5,34 1,28 Traditional Classroom Instruction (TCI) 31 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 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 in questions 2.3 and 2.5, determine the critical value for the test for a significance level of 5% (0,05). (1) IOP2601/Ass 03/Sem 2 2024_QP 2.7 Interpret the results in terms of the rejection or non-rejection of the null hypothesis and justify. (2) 2.8 Interpret your rejection or non-rejection of the null hypothesis in plain language, in terms of the original problem statement. (2) QUESTION 3 [15] A researcher from the University of Nairobi wants to investigate whether students’ perceptions of the effectiveness of online learning platforms change as they advance through the semester. The researcher randomly selects five (5) students who are enrolled in a course that utilises online learning tools and surveys their perceptions at the beginning, in the middle, and at the end of the semester. The scores obtained from the survey are provided in Table 2 below. Table 2 Perceptions of Online Learning Platforms Scores Beginning (X1) Middle (X2) End (X3) ƩX1 = 32 ƩX2 = 42 ƩX3 = 3