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 :

-1.25

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)

$⇒Z=\frac{34.25-35}{3/\sqrt{25}}$

$=\frac{-0.75}{3/5}=-1.25$