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.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -2
Given $μ_0 = 15, n = 50, \bar x = 14.15, σ = 3$
$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}=\frac{14.15-15}{\frac{3}{\sqrt{50}}}=\frac{-0.85×\sqrt{50}}{3}$
$=-2.003$
$∴Z=-2$