L. Planets 1S the name given to a hew boOX OI chocolates. kach box contains 18 chocolates and each chocolate is one of four types: Venus, Saturn, Jupiter and Neptune. The same number of each type is manufactured but a random process is used to fill the boxes. (a) Find the probability that a box contains no more than 7 Saturns. [2] Through online forums it is clear that Saturn is the most popular. In order to increase sales, the manufacturer claims to have increased the proportion of Saturns. You decide to test the manufacturer's claim by purchasing a box of Planets. (b) The box contains 8 Saturns. Does this support the manufacturer's claim at the 5% significance level? Write down your hypotheses clearly, state the p-value and show your working in full. [6]