In order to compare the means of two populations, independent random samples of 168 observations are selected from each population, with the following results:
(a) Use a 97% confidence interval to estimate the difference between the population means (μ₁ - μ₂).
≤ (μ₁ - μ₂) ≤
(b) Test the null hypothesis: H₀: (μ₁ - μ₂) = 0 versus the alternative hypothesis: Hₐ: (μ₁ - μ₂) ≠ 0. Using α = 0.03, give the following:
(i) the test statistic z =
(ii) the positive critical z score
(iii) the negative critical z score
The final conclusion is:
We can reject the null hypothesis (μ₁ - μ₂) = 0 in favor of the alternative (μ₁ - μ₂) ≠ 0.
There is not sufficient evidence to reject the null hypothesis (μ₁ - μ₂) = 0.
(c) Test the null hypothesis: H₀: (μ₁ - μ₂) = 21 versus the alternative hypothesis: Hₐ: (μ₁ - μ₂) ≠ 21. Using α = 0.03, give the following:
(i) the test statistic z =
(ii) the positive critical z score
(iii) the negative critical z score
The final conclusion is:
We can reject the null hypothesis (μ₁ - μ₂) = 21 in favor of the alternative (μ₁ - μ₂) ≠ 21.
There is not sufficient evidence to reject the null hypothesis (μ₁ - μ₂) = 21.
In order to compare the means of two populations, independent random samples of 168 observations are selected from each population, with the following results:
Sample 1 Sample 2
x₁ = 1 x₂ = 0
s₁ = 105 s₂ = 130
(a) Use a 97% confidence interval to estimate the difference between the population means (μ₁ - μ₂).
> (2T - In) 5
(b) Test the null hypothesis: H₀: (μ₁ - μ₂) = 0 versus the alternative hypothesis: Hₐ: (μ₁ - μ₂) ≠ 0. Using α = 0.03, give the following:
(i) the test statistic z =
(ii) the positive critical z score
(iii) the negative critical z score
The final conclusion is:
- We can reject the null hypothesis (μ₁ - μ₂) = 0 in favor of the alternative (μ₁ - μ₂) ≠ 0.
- There is not sufficient evidence to reject the null hypothesis (μ₁ - μ₂) = 0.
(c) Test the null hypothesis: H₀: (μ₁ - μ₂) = 21 versus the alternative hypothesis: Hₐ: (μ₁ - μ₂) ≠ 21. Using α = 0.03, give the following:
(i) the test statistic z
(ii) the positive critical z score
(iii) the negative critical z score
The final conclusion is:
- We can reject the null hypothesis (μ₁ - μ₂) = 21 in favor of the alternative (μ₁ - μ₂) ≠ 21.
- There is not sufficient evidence to reject the null hypothesis (μ₁ - μ₂) = 21.