A random sample of 500 houses in a certain suburb yielded 200 of which contained a 'fax' machine. Establish a 90% confidence interval for the true proportion of houses in this suburb which contain fax machines. Use the following template to answer this question. I. What is the parameter of interest? lI. What is the point estimator? III. What is the associated sampling distribution (how do you know this?). IV. Specify the formula for the 90% confidence interval estimator for the parameter. V. Perform the necessary calculations and write down the lower and upper limits of the 90% confidence interval. VI. Interpret the calculated confidence interval. (1 mark) VI. Describe what happens to the width of the confidence interval when the sample size decreases to 400, assuming that the sample proportion remains the same. VIII. Describe what happens to the width of the confidence interval when the confidence level increases to 95%, assuming the sample size is 500.