) A bottling machine fills up cola for 330ml cans. It is noted that the volume of the cola filled follows a normal distribution. To test the consistency of the machine, 20 discs are randomly selected and the mean volume is 327ml while the standard deviation is 2.8ml. What is the 99% confidence interval for the mean volume of the cola filled?

(b) A company claims that the LED bulbs it produces can last at least 50,000 hours. A sample of 20 bulbs show a mean of 49,000 hours and standard deviation of 5800 hours. It is assumed that the lifespan of the LED bulbs follows a normal distribution. Conduct a hypothesis testing using the critical value approach, at the 0.05 level of significance. Is there evidence that the company claim is true?