STAT2002: Assignment 2 This assignment is worth 20% of the grade for this unit Question 1 (5 marks). IQ is normally distributed, with a mean of 100 and a standard deviation of 15. A Psychology Honours student is conducting a study which involves completion of a survey on consumer attitudes and the measurement of IQ using Raven’s Progressive Matrixes. The average IQ of the student sample (n=25) is 112. The student wishes to know whether this is significantly different to the mean of the population. State the experimental and null hypotheses. (1 mark) Calculate the z-score of the obtained statistic on the sampling distribution of the mean. (1 mark) What is the probability of this z-score having been obtained if the null hypothesis were true? (1 mark) State what statistical decision you would come to on this basis. (1 mark) If it was important to the student’s research on consumer attitudes that the sample be representative of the normal population, what would be the implication of this outcome? (1 mark) Question 2 (5 marks). An academic researcher is evaluating the effectiveness of a new method of teaching statistics to University students. Last year, the mean mark obtained in her unit was 70%. This year her class has 16 students in it. The students are given special tutorials, which were not provided last year. The average mark at the end of session exam is 76%, and the estimate of the population standard deviation is 16%. Does this sample provide statistical evidence that the new method of teaching statistics is effective? Show all the steps of the logic of the hypothesis test you conduct. (2 marks) In Session 2 she is able to repeat her experiment, but this time there are 64 students enrolled in her unit. On this occasion, the mean exam mark following the teaching innovation is again 76%, and the estimate of the population is again 16%. Do these data support the researcher’s claim that the new method of teaching statistics is effective? Show all the steps of the logic of the hypothesis test you conduct. (2 marks) Explain why the outcome of test (a) might be different to that of test (b). (1 mark) Question 3 (5 marks). A variety of research results suggest that visual images interfere with visual perception. In one study, Segal and Fusella (1970) had participants watch a screen, looking for brief presentations of a small blue arrow. On some trials, the participants were also asked to form a mental image. Data similar to Segal and Fusella’s results are shown in the table below. Conduct an appropriate test to determine whether there is a significant difference between the conditions using SPSS. Cut-and-paste the output from your analysis into your report. (1 mark) Draw an appropriate figure illustrating the results of the experiment. (2 marks) Describe the outcome of the experiment as displayed in this figure, incorporating the results of the statistical analysis conducted. (2 marks) Question 4 (5 marks). A sample of problem gamblers were assigned to one of two conditions: a waiting-list control and debunking gambling myths (DGM) coaching session. Following the coaching session the two groups completed a gambling engagement test, providing a score out of 50 in which high scores indicate a high level of propensity to engage in gambling. Problem gambling is defined as a score of 25 or above on this scale. The data are shown below: Conduct an appropriate test to determine whether there is a significant difference between the groups using SPSS. Cut-and-paste the output from your analysis into your report. (1 mark) Draw an appropriate figure illustrating the results of the experiment. (2 marks) Describe the outcome of the experiment as displayed in this figure, incorporating the results of the statistical analysis conducted. Discuss the degree to which the coaching sessions have been successful. (2 marks)