Consider the following hypothesis test:
$H_0 : μ ≤ 25$
$H_a:μ>25$.
A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. What is the rejection rule using critical value? What is your conclusion? ($α$ = 0.01)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Reject $H_0$ if $Z≥2.33$; since $Z=1.48$, do not reject $H_0$
Given $μ_0 = 25, n = 40, \bar x = 26.4, σ = 6$ and $α=0.01$
$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}=\frac{26.4-25}{\frac{6}{\sqrt{40}}}$
$=\frac{1.4 × \sqrt{40}}{6}= 1.475 = 1.48$
$∴ Z=1.48$
Reject $H_0$ if $Z≥Z_α$ i.e. $Z≥Z_{0.01}$ i.e. $Z≥2.326$
$∵1.48<2.33$
So, do not reject $H_0$.