Help needed with detailed explanations

( 18 points) Bottiedluice A local bottler in Hawaii wants to average 15 ounces of passion fruit juice in each bottle. In order to analyze the bottling process they take a random sample of 36 bottles. The mean weight of passion fruitjuice in the sample is 14.8 ounces. You can assume that the precision ofthe filling machine results in a population standard deviation of 0.8 ounces. a) Using the mathematical symbols, give the null and alternative hypotheses to test if the bottling process is inaccurate. Ha: HA: b) Show the calculation of the test statistic c) Show the calculation of the p-value [either an exact value or a \"bracketed\" value) d) What should the juice bottler conclude (in context} if they test at the level of significance (1 = .05? e) If their conclusion is, in fact, wrong, are they making a Type I Error or a Type II Error? Explain briefly