Question 1070879: In a study examining the effect of environment on development, Krech and his colleagues (1962) divided a sample of infant rats into two groups. One group was housed in astimulus-rich environment containing ladders, platforms, tunnels, and colorful decorations. The second group was housed in stimulus-poor conditions consisting of plain gray cages. At maturity, maze-learning performance was measured for all the rats. Krech hypothesized that stimulus-rich rats would commit fewer errors than stimulus-poor rats. The following hypothetical data simulate Krech’s results. The scores are the number of errors committed by each rat before it successfully
solved the maze:
Rich Rats: 18, 24, 27, 23, 31, 29, 20, 33, 25, 30
Poor Rats: 37, 27, 26, 31, 35, 43, 40, 36, 28, 29
Conduct at-Test (one-tail, α = .01) for two Independent groups to see if there is a significant difference between the two groups
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Ho; mean of poor rats = mean of rich rats
H1; mean of poor rats > mean of rich rats
:
mean(u(1)) of rich rats = 26 and standard deviation(s(1)) = 4.876
mean(u(2)) of poor rats = 33.2 and standard deviation(s(2)) = 5.846
:
alpha(a) = 0.01
:
degrees of freedom(df) = (10-1) + (10-1) = 18
:
Use the t-table to look up a one-tailed test with 18 degrees of freedom and an alpha of 0.01. We find a critical value of 2.5524. Thus, our decision rule for this one-tailed test is:
If t is greater than 2.5524, reject the null hypothesis.
:
df(1) = 9 and df(2) = 9
:
s(1)^2(df(1)) = (4.876)^2 * 9 = 213.9784
s(2)^2(df(2)) = (5.846)^2 * 9 = 307.5814
:
S(p)^2 = (213.9784 + 307.5814) / (9 + 9) = 28.9755
:
t = (33.2 - 26) / square root( (28.9755/9) + (28.9755/9) ) = 2.8374
:
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t is > 2.5524, therefore we reject Ho which means that there is a significant difference between the groups of rats
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