Luki Corporation manufactures bottles of an organic energy booster which are supposed to contain a mean fill of 500 ml. The filling process follows a normal distribution. The company uses a filling machine,FIU17, which was a top seller when it was purchased. As the manager of Luki, you oversee the volume of drink put into the bottles so that each bottle is not overfilled leading to a reduction in profits. However, over the last few months, you have received many calls from your customers claiming that they were cheated because some bottles contained less than 500 ml. You took a random sample of 25 bottles which showed a mean fill of 497.84 ml and a standard deviation of 2.5 ml. Keep four decimal places and use a = 0.05. a) You contacted the company that sold you the FIU17. A new filling machine FIU20 has been introduced and you were offered a trade-in after a 5-day trial period. The filling process follows a normal distribution. You would opt for the FIU20 machine provided it would help to reduce customers' claims of being cheated, i.e., the mean fill should improve. You took a random sample of 25 bottles produced by FIU20, showing a mean of 500.64 ml and a standard deviation of 1.80 ml. Is there enough evidence to infer that there will be fewer customers' claims of being cheated if you opt for the FIU20 machine? b) Assume that 16 of the 25 sampled bottles using the FIU20 were correctly filled; 4 bottles were underfilled ( 500 ml). You construct an interval estimator for the proportion of bottles that was overfilled and obtained: LCL = 0.0684 and UCL - 0.3316. What level of significance would you have used? c) Suppose that you wanted to prove that the proportion of correctly filled bottles was more than 60%. If the test statistic z is calculated as 5.25, what is the corresponding p-value