In a two-sample t-test comparing lifetimes of halogen and incandescent bulbs, the null hypothesis states that the difference in means equals zero. Which statement expresses that null hypothesis?

In a two-sample t-test comparing lifetimes of halogen and incandescent bulbs, the null hypothesis states that the difference in means equals zero. Which statement expresses that null hypothesis?

• A. mu_halogen - mu_incandescent ≠ 0
• B. mu_halogen = mu_incandescent
• C. mu_halogen - mu_incandescent = 0
• D. mu_halogen > mu_incandescent

Answer: (C)

Null hypotheses express no effect or no difference. For a two-sample t-test comparing lifetimes, the null claim is that the two population means are the same, so the difference between them is zero. In notation, that’s mu_halogen - mu_incandescent = 0, which is also equivalent to mu_halogen = mu_incandescent. The other statements describe a difference or a direction of difference, which align with the alternative hypothesis in a two-sided test or a one-sided test, not the null.

Null hypotheses express no effect or no difference. For a two-sample t-test comparing lifetimes, the null claim is that the two population means are the same, so the difference between them is zero. In notation, that’s mu_halogen - mu_incandescent = 0, which is also equivalent to mu_halogen = mu_incandescent. The other statements describe a difference or a direction of difference, which align with the alternative hypothesis in a two-sided test or a one-sided test, not the null.