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.

1.48

The correct answer is Option (2) → 1.48

Given $μ_0 = 25, n = 40, \bar x = 26.4, σ = 6$

$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}=\frac{26.4-25}{\frac{6}{\sqrt{40}}}$

$=\frac{1.4 × \sqrt{40}}{6}= 1.475 = 1.48$

$∴ Z=1.48$