Question

A coworker claims that Skittles candy contains equal quantities of each color (purple, green, orange, yellow, and red). In other words, 1/5 of all Skittles are purple, 1/5 of all Skittles are green, etc. You, an avid consumer of Skittles, disagree with her claim. Test your coworker's claim at the α=0.10 level of significance, using the data shown below from a random sample of 200 Skittles.

Which would be correct hypotheses for this test?

H0:p1=p2

; H1:p1≠p2
H0:
Red Skittles are cherry flavored; H1:
Red Skittles are strawberry flavored
H0:
Taste the Rainbow; H1:
Do not Taste the Rainbow
H0:
Skittles candy colors come in equal quantities; H1:

Skittles candy colors do not come in equal quantities

Sample Skittles data:

Color   Count
Purple   38
Green   32
Orange   48
Yellow   47
Red   35

Test Statistic:

Give the P-value. Express to two decimal places:

Which is the correct result:

Do not Reject the Null Hypothesis
Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is not enough evidence to support the claim that Skittles colors come in equal quantities
There is not enough evidence to reject the claim that Skittles colors come in equal quantities.

Answer 1

H0:
Skittles candy colors come in equal quantities;

H1:Skittles candy colors do not come in equal quantities

Applying chi square goodness of fit tesT:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Purple	0.200	38	40.00	-0.32	0.100
Green	0.200	32	40.00	-1.26	1.600
Orange	0.200	48	40.00	1.26	1.600
Yellow	0.200	47	40.00	1.11	1.225
Red	0.200	35	40.00	-0.79	0.625
total	1.000	200	200		5.150

Test Statistic X² =5.150

p value =0.2722

Do not Reject the Null Hypothesis

There is not enough evidence to reject the claim that Skittles colors come in equal quantities.