Please answer part (4) in the following problem:

Problem 3. Tuition fee

A random sample of 30 full-time students form a large post-secondary institution was asked about their average tuition fee for the first year. From the data it was noted that the mean is $7850.00. The population standard deviation of the tuition fee is $257.00. Assume that the tuition fee is approximately normally distributed.

1. Construct an 80% confidence interval for . [3 marks]
2. Construct a 97% confidence interval for . [3 marks]
3. Refer to (a) and (b). What happens to the width of the confidence interval as the confidence level is increased (and everything else is kept the same)? [1 mark]
4. Refer to (a). Suppose you were not happy with the width of the confidence interval and wanted to cut the size of the interval to half, what should the sample size be? (Note: No calculation necessary!)
5. [1 mark]