Question

write the null and alternative hypothesis
h₀: μ₁ = μ₂ h₁: μ₁ < μ₂
h₀: μ₁ = μ₂ h₁: μ₁ > μ₂
h₀: μ₁ = μ₂ h₁: μ₁ ≠ μ₂

Explanation:

Step1: Recall hypothesis definitions

The null hypothesis \(H_0\) is a statement of no difference. The alternative hypothesis \(H_1\) is what we are trying to find evidence for.

Step2: Analyze the given options

• In hypothesis testing for comparing two means \(\mu_1\) and \(\mu_2\):
• The null hypothesis is \(H_0:\mu_1 = \mu_2\) (no difference between the means).
• The alternative hypotheses can be:
• \(H_1:\mu_1<\mu_2\) (left - tailed test).
• \(H_1:\mu_1>\mu_2\) (right - tailed test).
• \(H_1:\mu_1

eq\mu_2\) (two - tailed test).

Answer:

The three common pairs of null and alternative hypotheses for comparing two population means \(\mu_1\) and \(\mu_2\) are:

1. \(H_0:\mu_1 = \mu_2\) and \(H_1:\mu_1<\mu_2\)
2. \(H_0:\mu_1 = \mu_2\) and \(H_1:\mu_1>\mu_2\)
3. \(H_0:\mu_1 = \mu_2\) and \(H_1:\mu_1

eq\mu_2\)