Answer:
Step-by-step explanation:
Hello!
You are asked to test the difference of the population means of the opinion of men and women over a constitutional amendment to ban burning the national flag.
Population 1 (women)
Sample n₁= 400
X[bar]₁= 80.6
Population 2 (men)
n₂= 586
X[bar]₂= 77.6
σ₁= σ₂ = σ =3.5
To test whether there is a difference between the opinion of people about the amendment regarding their gender the hypothesis is:
H₀: μ₁ - μ₂ = 0
H₁: μ₁ - μ₂ ≠ 0
α: 0.05
The statistic to use is a pooled Z:
Z=<u> (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) </u> ~N (0;1)
σ*√(1/n₁ + 1/n₂)
The critical region for this hypothesis is two tailed:
Z=<u> (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) </u> = <u> (80.6-77.6) - 0 </u> = 13.215
σ*√(1/n₁ + 1/n₂) 3.5√(1/400 + 1/586)
Since the calculated Z-value is greater than the right critical value -81.96) the decision is to reject the null hypothesis. There is significant evidence to conclude that there is no difference between the population means of the opinion about the constitutional amendment to ban the burning of the national flag of women and men.
I hope it helps!