null & alternative hypothesis

Question

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Identify both the null and alternative hypothesis.

H₀: 𝜇 > 14 and H₁: 𝜇 ≤ 14

H₀: 𝜇 ≥ 14 and H₁: 𝜇 ≤ 14    

H₀: 𝜇 < 14 and H₁: 𝜇 ≥ 14

H₀: 𝜇 ≤ 14 and H₁: 𝜇 > 14

H₀: 𝜇 < 14 and H₁: 𝜇 > 14

H₀: 𝜇 ≤ 14 and H₁: 𝜇 ≥ 14

H₀: 𝜇 > 14 and H₁: 𝜇 < 14

H₀: 𝜇 ≥ 14 and H₁: 𝜇 < 14

Answer 1

Because the company is claiming that the mean weight of the cereal in its packet is at least 14 oz., that's what we are testing, which is the alternate hypothesis (H₁). We don't know if it's true or not. There's the possibility that the mean weight is less than 14 oz., which would be the null hypothesis (H₀), or the initial thought. Thus, the hypotheses would be set up like this:

H₀: μ<14 <-- Null Hypothesis

H₁: μ≥14 <-- Alternate Hypothesis

Thus, the third option from the list is correct!

Hope this helped!