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]