# 04_09_2 - 1 Alex buys a package of Sour Jelly Beans On the...

This preview shows pages 1–2. Sign up to view the full content.

Alex buys a package of Sour Jelly Beans. On the package, it says that 50% of all jelly beans are lemon, 30% are cherry, and 20% are lime. When Alex opens the package, he finds 15 lemon, 9 cherry and 12 lime jelly beans. a) Is there enough evidence to conclude that the true proportions are different from the ones listed on the package? Use α = 0.05. H 0 : p 1 = 0.50, p 2 = 0.30, p 3 = 0.20. H 1 : not H 0 . n = 15 + 9 + 12 = 36. E 1 = n p 10 = 36 × 0.50 = 18 . E 2 = n p 20 = 36 × 0.30 = 10.8 . E 3 = n p 30 = 36 × 0.20 = 7.2 . 1 2 3 Total O 15 9 12 36 E 18 10.8 7.2 36 ( ) E E O 2 - ( ) 18 18 15 2 - ( ) 10.8 8 . 10 9 2 - ( ) 7.2 2 . 7 12 2 - 0.5 0.3 3.2 4.0 3 – 1 = 2 degrees of freedom. 2 05 . 0 ( 2 ) = 5.991 . Q 2 = 4.0 < 5.991 = 2 α χ . Do NOT Reject H 0 . b) Assuming that the proportions listed on the package are correct, and that jelly beans are selected at random, what is the probability of having 15 lemon, 9 cherry and 12 lime jelly beans in a package? 12

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Spring '08