Question 1189908: To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with standard deviation of 5, and 50 girls averaged 62.8 with standard deviation of 4.6
a) Test, at alpha=0.05, whether the difference is significant or not.
b) Test if the difference is 3
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: mu boy=mu girl
Ha: mu boy NE mu girl
alpha=0.05 p{reject Ho|Ho true}
test is 2 sample t-test
df=98
critical value is 1.985
calculation t=(diff means/SE)
=(67.4-62.8)/sqrt (s1^2/n1)+(s2^2/n2))
=4.6/sqrt [(25/50+(21.16/50)]
=4.6/.96=4.79
reject Ho and conclude there is a difference between the two at the 0.05 level.
p-value <0.0001
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For difference of 3,
mu boy-mu girl <=3
mu boy-mu girl NE>=3
t-value is 3/0.96=3.125, so reject that hypothesis and say that the difference is greater than 3.
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