Question

Favorite Skittles Flavor?

A poll sampled 75 people, asking them their favorite skittle flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 98 people, again asking them their favorite skittle flavor, but rather than by color they asked by the actual flavor (lime, orange, grape, strawberry, and lemon, respectively). The table below shows the results from both polls. Does the way people choose their favorite Skittles type, by color or flavor, appear to be related to which type is chosen?

	Green (Lime)	Orange	Purple (Grape)	Red (Strawberry)	Yellow (Lemon)
Color	20	10	17	15	13
Flavor	15	18	22	33	10

Table 1 Skittles popularity

(a) Give a table with the expected counts for each of the 10 cells. Round your answers to two decimal places.

b) How many degrees of freedom do we have for this test?

c) Calculate the chi-square test statistic to 2 decimal places and the p-value to 4 decimal places.

Answer 1

Expected frequency of a cell = sum of row*sum of column / total sum                      

Chi-Square Test of independence
	Observed Frequencies
	0
0	green	orange	purple	red	yellow		Total
Color	20	10	17	15	13		75
Flavor	15	18	22	33	10		98
Total	35	28	39	48	23		173
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	green	orange	purple	red	yellow		Total
Color	35*75/173=15.173	28*75/173=12.139	39*75/173=16.908	48*75/173=20.809	23*75/173=9.971		75
Flavor	35*98/173=19.827	28*98/173=15.861	39*98/173=22.092	48*98/173=27.191	23*98/173=13.029		98
Total	35	28	39	48	23		173

a)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	green	orange	purple	red	yellow
Color	15.17	12.14	16.91	20.81	9.97
Flavor	19.83	15.86	22.09	27.19	13.03

b)

Number of Rows =   2
Number of Columns =   5
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 5- 1 ) =   4

c)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   7.86
      
      
p-Value =   0.0967 [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p value > α , do not reject Ho  

the way people choose their favorite Skittles type, by color or flavor, do not appear to be related to which type is chosen