Question 3 An analyst in a market research company would like to analyze the daily time spent on social media applications by HELP university students. Below are the time (hours) spent on social media applications and gender (M = male, F = female) of a group of 30 students. Time (hours) 1.5 2.0 2.4 5.1 0.8 2.6 3.1 4.7 1.8 2.0 3.8 2.5 0.5 1.8 2.6 Gender F F F M M F F M M F F F F M F Time (hours) 3.2 2.9 3.8 1.7 1.2 1.6 2.5 3.3 4.5 3.9 2.1 1.6 2.7 1.0 2.4 Gender M M M F F M F F F M M F F M F i. Find the probability that a randomly selected student spends between 2.1 hours and 3.9 hours per day on social media applications. (5 marks) ii. Find the probability that the mean daily time spent on social media applications for four randomly selected students is more than 2.8 hours. (3 marks) iii. Five students are randomly selected. Find the probability that less than three of them spend less than 3.2 hours per day on social media applications. (5 marks) iv. State the assumption(s) made in order to carry out the calculations in (i) to (iii). (2 marks) v. Past records show that HELP university students spent on average, 2.3 hours per day on social media applications. The analyst claims that the daily time spent has increased. Assume the standard deviation calculated in (i) remains the same for population, using the critical value method, can we accept the claim at 1% level of significance? (10 marks)