1 a developmental researcher compares 4 year olds and 8 year

1. a developmental researcher compares 4 year olds and 8 year olds on their ability to understand the analogies used in stories. The scores for the five 4 year olds tested were 7, 6, 2, 3, and 8. The scores for the three 8 year olds tested were 9, 2 and 5. Using the .05 level, do older children do better?

a) use the steps of hypothesis testing.

2. van aken and asendorpf studied 139 german 12 year olds. All of the children completed a general self worth questionnaire and were interviewed about the supportivness they experienced from their mothers, fathers and classmates. The researchers then compared the self worth of those with high and low levels of support if each type. The researchers reported that “lower general self wortj was found for children with a low supportive mother (t(137)= 4.52 p <.001, d(effect size) = 0.78) and with a low supportive father t(137) = 4.03, p < .001 d (effect size) = 0.69) a lower general self worth was also found for children with only low supportive classmates (t(137) = 2.04 p < .05 d (effect size) = 0.35) d in the above is a symbol for effect size.

a) Explain what these results mean to a person who has never had a course in statistics

b) Include a discussion of effect size and power

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 > u2
Alternate, older children do better - H1: u1 < u2
Test Statistic
X(Mean)=5.2
Standard Deviation(s.d1)=2.588 ; Number(n1)=5
Y(Mean)=5.33
Standard Deviation(s.d2)=3.5118; Number(n2)=3
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.2-5.33/Sqrt((6.69774/5)+(12.33274/3))
to =-0.06
| to | =0.06
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 2 d.f is 2.92
We got |to| = 0.05568 & | t | = 2.92
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Left Tail - Ha : ( P < -0.0557 ) = 0.48033
Hence Value of P0.05 < 0.48033,Here We Do not Reject Ho

we have evidence to indicate that there is no-Significance between them