Find the value of the test statistic z using z=^p−p√pq/n.
The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.
Given:
p = 0.15 (proportion of elderly deaths attributable to residential falls)
q = 1 - p = 1 - 0.15 = 0.85
n = 800
Hypothesized proportion, p̂ = 0.10
Using the formula for the test statistic z:
z = (p̂ - p) / √(p*q / n)
z = (0.10 - 0.15) / √(0.15*0.85 / 800)
z = (-0.05) / √(0.1275 / 800)
z = -0.05 / √0.000159375
z = -0.05 / 0.012625
z = -3.968
Therefore, the value of the test statistic z is -3.968.