Question

A psychologist has measured the IQ for a group of 30 children, now in the third grade, who had been regularly exposed to a new interactive, computerized teaching device. The mean IQ for these children is X = 106.

a. Test the null hypothesis that these children are no different from the general population of third-graders (μ = 100, σ = 6) using alpha = .05.

Answer 1

$H_0:a=100$

$H_1:a\not=100$

Test statistic: $T={\frac {(X-a)*\sqrt{n}} {\sigma}}={\frac {(106-100)*\sqrt{30}} 6}\approx 5.48$

Since the population standard deviation is known, then it is appropriate to use z-score as critical value. So, $P(Z>Cr)={\frac {\alpha} 2}=0.025\implies Cr=1.96$

Since $T\notin (-Cr,Cr)=(-1.96,1.96)$ , then we should conclude that, based on the given data, there is enough evidence to reject the null hypothesis and admit that average group IQ is different from population's