Answer:
The proportion of smokers was higher in 1990 than in 2000
Step-by-step explanation:
Solution
Recall that,
The total number of sample 1 (n1) = 1000
Total sample 2 number (n2) = 2000
The number of favourable events (X1) = 300
The number of favourable events (X2) = 500
so,
p₁ = X₁/n₁ = 300/1000 = 0.3
p₂ = X₂/n₂ =500/2000 =0.25
α = 0.05
We are interested in testing the hypothesis.
The hypothesis (Null) ....> H₀ : p₁ = p₂
Alternate hypothesis------ > H₁ : p₁ > p₂
Thus,
P = X₁ + X₂/ n₁ + n₂
P =300 + 500/1000 +2000
P =800/3000
=0.2667
Now,
Z₀ = P₁ - P₂/√ P (1 -P) (1/n₁ + 1/n₂)
Z₀ = 0.3 - 0.25/√0.2667 (1 - 0.2667) (1/1000 + 1/2000)
Z₀ = 0.4999999999999999/√ 0.2667 (0.7333000000000001) (0.001 +0.0005)
Then,
Z₀ = 0.4999999999999999/√0.00029335666500000004
Z₀ = 2.9193
so,
zα/2 = z0.05/2 =z0.025
zα/2 = 1.6448536269514722
Now, we apply the decision rule:
Decision Rule: Reject the null hypothesis if the statistic value test is higher than the critical value 1.6448536269514722
The statistic value, 2.9193 is greater than the critical value 1.6448536269514722, then we will reject the null hypothesis.
Therefore, the proportion of smokers was higher in 1990 than in 2000
(approximately)