Chloe opens another smaller package from the same company, which is also supposedly 20% almonds (A), 30% cashews (C), 10% macadamias (M), and 40% peanuts. Out of 20 nuts, she find that there are 12 peanuts
a. Chloe wants to directly calculate the exact p-value of this occurring! (i. e. she does not want to do a proportion test). Please perform this test for Chloe at a = 0.05. Show/explain how to set up this problem, and you may use a table or calculator to get the answer. Note: We can not use normal or chi squared approximate tests to calculate exact p-values
b. Suppose the company's claim about its distribution of nuts is true. Given the following weights, use the central limit theorem to calculate the (approximate) probability that a random sample of 100 nuts has a sample mean that weighs less than 1g:
1. Almond: 19
2. Cashew: 1.59
3. Macadamia: 2.5g
4. Peanut: 0.59