1)Jack 'n Jill, a company that produces snack foods , uses a machine to package 453oz bags of potato chips . Assuming that the net weights are normally distributed with sample mean 449oz with the standard deviation of all such weights is 7.8oz, they want to test if the machine is working properly. A random sample is checked. The weights are as follows: 460, 445, 420, 430, 450, 435, 416, 490, 488, 450, 455.

Does the sample provide sufficient evidence to conclude that the packaging machine is not working properly at a 5% level of significance?

2)Find the 99% Confidence Interval of the mean for the incomes of executive secretaries in Makati City. A random sample of 30 executive secretaries is given with standard deviation 4.07 and mean 18.3

3) The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 10 minutes. Based on discussions you have had with friends who have complained on how long they waited to be seen in the ER over a weekend, you dispute the administrator's claim. You decide to test your hypothesis. Over the course of a few weekends, you record the wait time for 41 randomly selected patients. The average wait time for these 41 patients is 11 minutes with a standard deviation of 3 minutes. Do you have enough evidence to support your hypothesis that the average ER wait time exceeds 10 minutes? You opt to conduct the test at a 1% level of significance.