Consider the following hypothesis test :
$H_0: \mu ≤ 35$
$H_a : \mu > 35$
A sample of 25 provided a sample mean of 34.25. The population standard deviation is 3. The value of the statistics is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → -1.25
The z-test formula,
$Z=\frac{\bar x-μ_0}{σ/\sqrt{n}}$
$\bar x$ = Sample mean = 34.25
$μ_0=35$
$σ=3$ (Population standard deviation)
$n=25$ (Sample size)
$⇒Z=\frac{34.25-35}{3/\sqrt{25}}$
$=\frac{-0.75}{3/5}=-1.25$