A baker claims that his baguettes weigh an average of 300g, but a consumer affairs inspector takes a random sample of 50 baguettes and discovers that the average weight of the sample is only 291g. As a consultant statistician, you are asked to determine whether the result of this sample is sufficient evidence to disbelieve the baker's claim. We assume that the bread weight follows a normal distribution with standard deviation of 20g and unknown mean u. Let X; be a random variable representing the weight of the i-th baguette. (a) What is a sensible estimator for u? (b) Formulate an appropriate null hypothesis Ho and alternative hypothesis H1. (c) Write down the test statistic and its distribution under the null hypothesis (d) Calculate the P-value based on the data. (e) With a level of significance a = 0.01, state your conclusion.. (f) Interpret your conclusion in the relevant context. standard function logic vector abc unit .....JPg W O 12.C Clear ~ } 0 (7 4:)