Answer
We can not reject the null hypothesis as there is no sufficient evidence that the mean is not equal to 50.
Work Step by Step
Here we have $H_{o}$: μ = 50, $H_{1}: μ \ne 50$, n = 15, x̅ = 48.1, s = 4.1, df = n-1 = 14 and α = 0.05
Using the Classical approach:
Using Table VI, we have: t = 2.145
$σ_{ x̅} = \frac{s}{\sqrt n} = \frac{4.1}{\sqrt 15} = 1.06$
$t = \frac{48.1 - 50}{1.06} = -1.79$
Since, -2.145 < -1.79 < 2.145, we fail to reject the null hypothesis.
