Question

A developmental researcher has observed that in a random sample of 60 toddlers, 27 preferred blue toys, 19 preferred red toys, and 14 preferred green toys. Perform a chi-square test of the null hypothesis that, in the entire population of toddlers, the preference for these three colors is equally divided.

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H0: Data follows the given distribution.

Alternative hypothesis: Ha: Data do not follow the given distribution.

We assume/given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

We are given

Number of categories = N = 3

Degrees of freedom = df = N - 1 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Color	Prop.	O	E	(O - E)^2/E
Blue	0.333333	27	20	2.45
Red	0.333333	19	20	0.05
Green	0.333333	14	20	1.8
Total	1	60	60	4.3

Test Statistic = Chi square = ∑[(O – E)^2/E] = 4.3

χ2 statistic = 4.3

P-value = 0.116484158

(By using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that Data follows the given distribution.

There is sufficient evidence to conclude that the preference for these three colors is equally divided.