SOLUTION: a fourth-grade teacher is told that 12 of his students are “gifted,” as determined by IQ tests, and the remaining 12 are not. In reality, the two groups have been carefully mat

Question 1165054: a fourth-grade teacher is told that 12 of his students are “gifted,” as determined by IQ tests, and the remaining 12 are not. In reality, the two groups have been carefully matched on IQ and previous school performance. At the end of the school year, the gifted students have a grade average of 87.2 with s = 5.3, whereas the other students have an average of 82.9, with s = 4.4. Perform a t-test to decide whether you can conclude from these data that false expectations can affect student performance; use alpha = .05, two-tailed.
can somoenone show the complete solutions and hypothesis? Thank you so much
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
I would like to assume that the students were treated the same, or even better, neither the teachers nor the students knew what group they were in.
Ho: gifted=regular
Ha: gifted not = regular
alpha=0.05 P{reject Ho|Ho true}
test is t two tailed df=22
critical value is |t|>2.074
test is (xbarG-xbarR)/sqrt [(s1^2/n1)+(s2^2/n2)]
the denominator is sqrt (2.341+1.613)=1.988
numerator is 4.3
t=2.163
This is greater than 2.074 so reject Ho and conclude the two populations are different.
p-value=0.042.

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