Skittles® Statistics teacher Jason Mole sky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: “The original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is $20$ percent of each flavor.”
a. State appropriate hypotheses for a significance test of the company’s claim.
b. Find the expected counts for a random sample of $60$ candies.
c. How large a $χ 2$ test statistic would you need to have significant evidence against the company’s claim at the α=0.05 level? At the $α = 0.01$ level?
d. Create a set of observed counts for a random sample of $60$ candies that gives a $P -$ value between $0.01$ and $0.05$ Show the calculation of your chi-square test statistic.

Question

Accepted Answer

Part (a) $H_{0} : p_{l e m o n} = 0.20, p_{l i m e} = 0.20, p_{o r a n g e} = 0.20, p_{s t r a w b e r r y} = 0.20, p_{g r a p h} = 0.20$

$H_{a} : A t l e a s t o n e o f t h e p_{i} ’ s i s i n c o r r e c t .$

Part (b) Expected count for each flavor is $12$

Part (c) If chi square statistic is greater than above critical values at specified level of significance then reject $H_{0}$

Part (d)

Short Answer