Question 3 (11 marks)

A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was taken of 10 one-bedroom units within a half-mile of the campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. We assume the population for one-bedroom units is normally distributed.

Your task is to construct a 95% confidence interval for the average rent per month for the population by addressing the following:

1. Parameter of interest (0.5 mark)
2. Point estimator (0.5 mark)
3. Sampling distribution of the point estimator (0.5 mark)
4. Specify the formula for the 95% confidence interval estimator for the parameter (1 mark)
5. Perform the necessary calculations and write down the lower and upper limits of the confidence interval 3 marks)
6. Interpret the calculated confidence interval (2 marks)
7. Briefly explain what would happen to the width of the interval in each case: (i) the sample size increased, (ii) the sample standard deviation increased, and (iii) the level of confidence increased (3 marks)