Question

A manufacturer produces five types of toys: Teddy Bear, Hello Kitty, Elsa, Anna and Superman. He wants to test that kids’ choices of these toys are not random. He conducted a survey to ask 10,000 kids to select one of their favorite toy. The result is summarized in the following table.

Teddy Bear	Hello Kitty	Elsa	Anna	Superman
750	2130	3020	2950	1150

Conduct a Chi Square Goodness-of-Fit test to test that kids do not select toys randomly. Use the significance level of 0.05

Answer 1

If the toy selection is random then the expected probability of selection of each type of toy = 1/5 = 0.20

Expected frequency for each type of toy = 0.20*10000 = 2000

Step 1: The null an alternative hypothesis are:

H0: p1 = p2 = p3 = p4 = p5 = 0.20 (The selection is random)

H1: At least one of the p1, p2, p3, p4, and p5 is note equal to 0.20 (The selection is not random)

Step 2: Test statistic

Test Statistic Chi Square = Sum of all Diff. sq./Exp. Fr. = 2122.400

Step 3: Critical Chi square value

Degrees of Freedom df = n-1 = 5-1 = 4

α = 0.05

Critical chi square value for α = 0.05 and df = 4 is obtained using critical value calculator. Screenshot below:

Critical chi square value = 9.4877

Step 4: Decision

Since Test Statistic Chi Square = 2122.400 > Critical chi square value = 9.4877, we reject null hypothesis

Step 5: Conclusion

At 0.05 significance level, there is enough evidence to claim that kids’ choices of these toys are not random.