Answer
The director of Institutional Research is testing whether the mean IQ of students is greater than 102. Since we fail to reject the Null Hypothesis, there is insufficient evidence that the mean IQ score of the students is greater than 102.
Work Step by Step
Here we have: $H_{o}$: μ = 102, $H_{a}$: μ > 102, n = 40, x̅ = 103.4, s = 13.2 and α = 0.05
Using the Classical approach:
Using Table VI, we have: t = 1.685
$σ_{ x̅} = \frac{s}{\sqrt n} = \frac{13.2}{\sqrt 40} = 2.087$
$t = \frac{103.4 - 102}{2.087} = 0.671$
Since, 0.671 < 1.685, we fail to reject the Null hypothesis.
