Question

A developmental psychologist is studying cognitive functions in children. Three-, four-, and five-year-olds are asked to choose between one large cookie or three smaller cookies that add up to only about half the mass of the large cookie. The number of children choosing each alternative is shown for each age group below:

	Three Years	Four Years	Five Years
One cookie	5	8	14
Three cookies	15	12	6

  
What is the p value that corresponds to the chi-square statistic for these data?

		> .05
		between .05 and .025
		between .025 and .01
		< .01

Suppose that the data for a chi-square test are as shown in the table below:

f o	14	8	11	5	6
f e	10	8	6	8	12

  
What is the p value that corresponds to the chi-square statistic for these data?

		> .05
		between .05 and .025
		between .025 and .01
		< .01

Answer 1

1)

Applying chi square test of independence:

	one cookie	5	8	14	27
	three cookie	15	12	6	33
	total	20	20	20	60
Expected	Ei=row total*column total/grand total	3 year	4 year	5 year	Total
	one cookie	9.000	9.000	9.000	27
	three cookie	11.000	11.000	11.000	33
	total	20	20	20	60
chi square    χ2	=(Oi-Ei)2/Ei	3 year	4 year	5 year	Total
	one cookie	1.778	0.111	2.778	4.6667
	three cookie	1.455	0.091	2.273	3.8182
	total	3.2323	0.2020	5.0505	8.485
test statistic X2 =		8.485
p value =		0.014

Correct option is: between .025 and .01

2)

applying chi square goodness of fit test:

observed	Expected	residual	Chi square
Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
14.0000	10.00	1.26	1.600
8.0000	8.00	0.00	0.000
11.0000	6.00	2.04	4.167
5.0000	8.00	-1.06	1.125
6.0000	12.00	-1.73	3.000
44	44		9.8917

test statistic X2 =		9.8917
p value =		0.0423

between .05 and .025