Question

A developmental psychologist is examining problem solving ability for grade school children. Random samples of 5-year-old, 6-year-old, and 7-year-old are obtained and a set of problems are given to them. The number of errors is reported below.

Number of errors

5-year-olds	6-year-olds	7-year-olds
32	31	18
31	21	21
24	19	24
15	18	21
34	30	20
23	26	16
17	25	15
18	23	26
21	18	17
20	15	18
19	24	17
30	25	15

A.        State the Independent Variable and the Dependent Variable.

B.        State the null hypothesis in words and symbols.

C.        Compute the appropriate statistic.

D.        What is your decision?

E.         State the full conclusion in words, after computing, if necessary multiple comparisons .

Answer 1

A. here  the Independent Variable age of school children and the Dependent Variable number of errors

B. the null hypothesis in words is there is no difference between the age of children for making number of errores

In symbols.

Ho:u( 5 year old) =u( 6 year old)= u( 7 year old)

using excel>data>data analysis >one way anova

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
5-year-olds	12	284	23.66667	42.24242
6-year-olds	12	275	22.91667	24.08333
7-year-olds	12	228	19	12.18182
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	150.7222	2	75.36111	2.879765	0.070345	3.284918
Within Groups	863.5833	33	26.16919
Total	1014.306	35

C. the appropriate statistic is F =2.879

D. decision :do not reject Ho because p value is less than 0.05

E.        conclusion : we have sufficient evidence to conclude that number of errors made by the children is same for every age given. Here it is not necessary to do multiple comparisons becasue all means are equal