Discuss the below:
Q1.You are visiting Dad's Root Beer Plant in Oakland. You are asked by the plant supervisor to determine if the Dad's Brand soda machines are correctly dispensing 32 ounces of root beer. In the past, the equipment was assumed to be not working properly if the cans were over-filled or under-filled. You observe the machine filling 9 bottles and collected the data. You are 95% sure that the machine is filling the bottles correctly. The amount dispersed is assumed to be normally distributed:
32.12 32.04 32.04
32.13 32.05 32.05
32.22 31.89 32.20
Q2. You are given the following information, find the Z-statistic: (95% level of confidence) based on the Z-test
Xbar = 980
U = 1000
Sample stdev = 50
N = 36
Q3. The average running time for current Broadway shows is 2 hours and 12 minutes. A producer in another city claims that the length of time of productions in his city is the same. He samples 8 shows and finds the time to be 2 hours and 5 minutes with a standard deviation of 11 minutes. At 95% level of confidence is the producer correct (NY Times Arts and Leisure)? Keep in mind, your numbers must be in minutes.
Q4. Find the T-critical if N = 22 at 95% level of confidence and 90% level of confidence
Q5.The average salary of graduates entering the actuarial field is reported to be $40,000. You sample 20 graduates and find the average salary to be $43,228 with a standard deviation of $4,000. At a 95% level of confidence is the statement regarding the average salary of $40K an accurate statement?