The null and alternate hypothesis will be;
Ho : µ ≥ 45
H1: µ < 45
Z-calculated = (x- µ)/ δM
x is the obtained mean score which is 36.4
µ is the mean that was hypothesized which is 45
δM is the standard error that is calculated by δ/√n = 4/√100 = 0.4 Continue reading...
Z-calculated = (36.4- 45)/0.4 = -21.5
It is a one tailed test since we are only interested as to whether the mean age has decreased. For a one tailed test, at α = 0.05; the z critical values are +/- 1.650.
The z obtained falls within the rejection region. We should reject the null hypothesis and accept the alternate hypothesis. Therefore,