Answer
We fail to reject the Null Hypothesis. The sample mean of 519 is not significantly higher than 515. In large samples, the P value will become smaller, making it more likely that the null hypothesis will be rejected.
Work Step by Step
Here we have: $H_{o}$: μ =515, $H_{1}: μ > 515$, n = 400, x̅ = 519, s = 111 and α = 0.05
Using the Classical approach:
Using Table VI, we have: t = 1.282
$σ_{ x̅} = \frac{s}{\sqrt n} = \frac{111}{\sqrt 400} = 5.55$
$t = \frac{519 - 515}{5.55} = 0.721$
Since, 0.721 < 1.282, we fail to reject the Null hypothesis.
