Question 11 A manufacturer of cereal wants to test the performance of one of its filling machines. The machine is designed to discharge a mean amount of 12 ounces per box, and the manufacturer wants to detect any departure from his setting. This quality study calls for randomly sampling of 100 boxes from production run to determine whether the average fill for the run is 12 ounce per box, The sample mean measured is 12.15 ounce per box and standard deviation is 0.51. Based on this information, can we conclude at 5% significant level that there has been a significant shift in average fill per box?

(a)What are the alternative hypothesis and null hypothesis?

(b)With level of significance of 5%, conduct a hypothesis testing. Can we conclude that there has been a significant shift in in average fill per box?

Calculate the p-value. Can we conclude that there has been a significant shift in in average fill per box at the level of significance of 5% by using the p-value?