Question

Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter.

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 46°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is les than 39 degrees.
Group of answer choices

Answer 1

The null hypothesis (H0) is that the mean temperature μ is equal to 46°F, and the alternative hypothesis (H1) is that the mean temperature μ is less than 39°F, indicating a left-tailed test.

Step-by-step explanation:

The manufacturer claims that the mean temperature μ of refrigerators is 46°F. The brewery owner believes that the mean temperature is less than 39°F. We need to express the null hypothesis (H0) and the alternative hypothesis (H1) in symbolic form.

Here, the null hypothesis represents the manufacturer's claim, and the alternative hypothesis represents the owner's belief. Therefore, the null and alternative hypotheses in symbolic form are:

• H0: μ = 46 (The true mean temperature is 46°F)
• H1: μ < 39 (The true mean temperature is less than 39°F)

It's important to note that the null hypothesis often involves equality (e.g., '=', ≥, or ≤), and the alternative hypothesis involves an inequality (e.g., '<', '>', or ≠). In this case, since we are testing whether the mean temperature is less than a certain value, it is a left-tailed test.