ERSH 6300 Homework 4 Assignment

2. Ribena is a juice-avored drink, popular in Europe and Australia. Ribena is avored withblack currant, a type of blackberry fruit that became popular during WW II as a substitutefor oranges. Black currant in its natural form is high in vitamin C, so Ribena has been widelymarketed as being healthy. However, like most juice drinks, Ribena has very little actualfruit juice.Ribena juice claimed on the package that it contains 7 mg of vitamin C per serving.In 2004, as part of a science fair project, two 14-year old Australian girls, Jenny Suo and AnnaDevathasan, decided to test samples of Ribena for vitamin C content.The girls tested a sample of n=11 packages of Ribena, and found an average of zero vitaminC in the sample.[In a later interview, they said that, after testing the very rst package and nding no vitaminC, they were so surprised, We just couldnt believe it. We thought we must have done itwrong. … We tested … another 10 times.]The company that makes Ribena (GlaxoSmithKline) said that the result must just have beendue to bad luck, and that all eleven packages must have been old or poorly sealed. But after alawsuit against the company, GlaxoSmithKline was found guilty of false and misleading claims;and in 2007, the company was ned $227,5001 .We can verify their results with a formal hypothesis test.(a) Write the formal hypotheses to test whether Ribena drink overall contains the claimedaverage vitamin C value, or whether it contains less than the claimed value. Be sure touse the appropriate parameter symbol.H0 :Ha :(b) For the purpose of the hypothesis test, we will assume that the 11 packages were sampledrandomly; and we will assume that the distribution of vitamin C among all Ribena packages is Normal (this assumption is necessary since the sample size is small). Also, assumethat the standard deviation of vitamin C in the population of all packages is = 4 mg(this assumption is reasonable for fruit-based foods).See for instance: http://www.scoop.co.nz/stories/BU0703/S00478.htm(Part b continued….)Graphically represent the resulting sampling distribution of the appropriate statistic assuming the Null Hypothesis is true. Label the center of the distribution with the appropriate value; and report the standard deviation of the distribution. Then mark the valueof the sample statistic in the appropriate location on the sketch, and shade the associatedtail probability. [You should notice that the direction of the tail matches the direction ofthe inequality chosen for the alternative hypothesis.](c) Calculate and report the p-value (Using Excel or a Normal Table as needed).(d) Draw a formal conclusion at the 1% signicance level; then, briey state the meaning ofyour conclusion in the context of the question regarding whether Ribena drink containsthe claimed amount of Vitamin C on average, or whether it contains less.