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)

1. Perform the necessary calculations and write down the lower and upper limits of the confidence interval (3 marks)
2. Interpret the calculated confidence interval (2 marks)
3. 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)

ANSWER:

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: A. B. C. D. Parameter of interest (0.5 mark) Point estimator (0.5 mark) Sampling distribution of the point estimator (0.5 mark) Specify the formula for the 95% confidence interval estimator for the parameter (1 mark) Perform the necessary calculations and write down the lower and upper limits of the confidence interval (3 marks) Interpret the calculated confidence interval (2 marks) 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