Consider the following hypothesis
$H_0: μ = 35$
$H_1: μ ≠35$
A sample of 81 items is taken whose mean is 37.5 and the standard deviation is 5. Test the hypothesis at 5% level of significance
(Given: Critical value of Z for a two-tailed test at 5% level of significance is 1.96)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Reject $H_0$; the population mean is significantly different from 35
Given $μ_0 = 35, \bar x = 37.5, n = 81, σ = 5$
$Z=\frac{\bar x-μ_0}{\frac{σ}{\sqrt{n}}}⇒Z=\frac{37.5-35}{\frac{5}{\sqrt{81}}}=\frac{2.5 × 9}{5}$
$⇒Z=4.5$
For a two tailed test $α = 0.05$ and
$Z_{α/2} = 1.96$ (given)
Since $Z = 4.5 > Z_{α/2}$
So, reject $H_0$.