Consider the following hypothesis test:

$H_0: μ = 15$

$H_a: μ ≠ 15$.

A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. Compute the value of the test statistic.

-2

The correct answer is Option (2) → -2

Given $μ_0 = 15, n = 50, \bar x = 14.15, σ = 3$

$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}=\frac{14.15-15}{\frac{3}{\sqrt{50}}}=\frac{-0.85×\sqrt{50}}{3}$

$=-2.003$

$∴Z=-2$