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. Compute the value of the test statistic.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.48
Given $μ_0 = 25, n = 40, \bar x = 26.4, σ = 6$
$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}=\frac{26.4-25}{\frac{6}{\sqrt{40}}}$
$=\frac{1.4 × \sqrt{40}}{6}= 1.475 = 1.48$
$∴ Z=1.48$