Question

The manufacturer of children's raincoats wants to know if there is a preference among children for any specific color. The information below is the color preference for a sample of 57 children between the ages 6 and 10.

Color	Frequency
Blue	24
Red	7
Green	10
Yellow	16

(a)	State the decision rule for 0.02 significance level. (Round your answer to 3 decimal places.)
	H0 : There is no preference for any color.
	H1 : There is a preference for some color.

Reject H0 if χ2>

(b)	Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

(c)	Is there any preference among children for any specific color? Use the 0.02 significance level.

   (Click to select)Do not rejectReject H₀. There is (Click to select)a preferenceno preference among children for any specific color.

Answer 1

Expected proportion = 1/4 =0.25

Category	Observed Frequency (O)	Expected Frequency (E)	(O-E)²/E
Blue	24	57 * 0.25 = 14.25	(24 - 14.25)²/14.25 = 6.6711
Red	7	57 * 0.25 = 14.25	(7 - 14.25)²/14.25 = 3.6886
Green	10	57 * 0.25 = 14.25	(10 - 14.25)²/14.25 = 1.2675
Yellow	16	57 * 0.25 = 14.25	(16 - 14.25)²/14.25 = 0.2149
Total	57	57	11.8421

a) Null and Alternative hypothesis:     

H0 : There is no preference for any color.

H1 : There is a preference for some color.            

df = n-1 = 3

Critical value:  

χ²α = CHISQ.INV.RT(0.02, 3) = 9.8374  

Reject Ho if χ² > 9.837

b) Test statistic:  

χ² = ∑ ((O-E)²/E) = 11.842

c) Reject H0. There is a preference among children for any specific color.