Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, σ) for the indicated parameter.

Question

The manufacturer of a refrigerator system of a refrigerator system for soda machines produces refrigerators that are supposed to maintain a true mean temperature, μ, of 43°F, ideal for a certain type of soda. The manufacturer of the soda does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

A) H_0: μ = 43° H_1: μ ≠ 43°
B) H_0: μ ≠ 43° H_1: μ = 43°
C) H_0: μ ≥ 43° H_1: μ < 43°
D) H_0: μ ≤ 43° H_1: μ > 43°

Answer 1

In this scenario, we have a manufacturer of a refrigerator system that claims the true mean temperature, μ, is 43°F, while the manufacturer of the soda believes that this claim is incorrect. To test this hypothesis, the null hypothesis (H₀) usually represents the status quo or the claim being tested, and the alternative hypothesis (H₁) represents the claim that contradicts the null hypothesis.

In symbolic form, the correct expressions are:

A) H₀: μ = 43° (the null hypothesis stating that the true mean temperature is 43°F) H₁: μ ≠ 43° (the alternative hypothesis stating that the true mean temperature is not equal to 43°F)

Therefore, the correct option is: A) H₀: μ = 43° H₁: μ ≠ 43°