Answer:
z(s) is in the rejection region we reject H₀ μ₁ = μ₂ and support the claim that at CI 95 % the means of the two groups differs
Step-by-step explanation:
Sample 1:
Sise sample n₁ = 115
μ₁ = 169,9 mmHg
σ₁ = 24,8 mmHg
Sample 2:
Sise sample n₂ = 235
μ₂ = 163,3 mmHg
σ₂ = 25,8 mmHg
We can develop a test hypothesis for differences in means to investigate if the mean peak systolic blood pressure differs between these two groups
We will choose CI = 95 % then significance level α = 5 %
α = 0,05 α/2 = 0,025
z(c) for 0,025 is from z-table z(c) = 1,96
Test Hypothesis:
Null Hypothesis H₀ μ₁ = μ₂
Alternative Hypothesis Hₐ μ₁ ≠ μ₂
The alternative hypothesis tells us that the test is a two-tail test.
z(s) = ( μ₁ - μ₂ ) / √ σ₁²/n₁ + σ₂²/n₂
z(s) = ( 169,9 -163,3 ) / √ (24,8)² /115 + ( 25,8)²/235
z(s) = 6,6 / √5,35 + 2,83
z(s) = 6,6 / 2,86
z(s) = 2,30
Comparing |z(c)| and |z(s)|
z(s) > z(c)
z(s) is in the rejection region we reject H₀ μ₁ = μ₂ and support the claim that at CI 95 % the means of the two groups differs
