Question 3

(a)In studying the amount of time that students of Institution X spend on part-time job per week, a random sample of 25 students is taken and their mean and standard deviation are 125 minutes and 20 minutes, respectively. Construct a 95% confidence interval for the mean amount of time for all students of Institution X spend on part-time job per week. State your assumption(s) and / or approximation(s). [8 marks]

(b)Suppose the amount of time spent by retired people watching TV per day is approximately normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. What is the probability that the average number of hours spent watching TV per day by a random sample of 5 retired people is more than 7 hours? [5 marks]

(c)A market research analyst has randomly selected 140 customers and 42 of them can identify the brand of a laundry detergent based on the shape of container. Construct a 95% confidence interval for the population proportion of customers who can identify the brand of laundry detergent based on the shape of container. [4 marks]