Q1. Review the following video. According to the video problem, you are required to do:

a. Please take a piece of paper and write down the process of establishing confidence intervals for the problem in the video step by step. Please notice the video provided the answer, but with a calculator. The expectation is you solve it with a formula, according to your understanding. Do not show the process with the calculator again. 

b. According to past experience, 18% of students took public transportation. Test if the situation changed. Solve the problem step by step.

Confidence Interval for a Population Proportion

https://www.youtube.com/watch?v=np-CwMl-O1M&t=3s

Q2. A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 6000 hours and a standard deviation of 400 hours. 

a. A random sample of 16 bulbs had an average life of 5850 hours. Is the manufacturer’s claim correct?

b. How about a random sample of 16 bulbs having an average of 5800 hours? What is your conclusion?