Express the Null Hypothesis and the Alternative Hypothesis in Symbolic $( \mu , p , \sigma )$

question 24

Multiple Choice

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $48 ^ { \circ } \mathrm { F } ,$ 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 incorrect.

• A) \(\begin{array} { l }
• H _ { 0 } : \mu = 48 ^ { \circ } \\
• H _ { 1 } : \mu \neq 48 ^ { \circ }
• \end{array}\)
• B) \(\begin{array} { l }
• H _ { 0 } : \mu \neq 48 ^ { \circ } \\
• H _ { 1 } : \mu = 48 ^ { \circ }
• \end{array}\)
• C) \(\begin{array} { l }
• H _ { 0 } : \mu \leq 48 ^ { \circ } \\
• H _ { 1 } : \mu > 48 ^ { \circ }
• \end{array}\)
• D) \(\begin{array} { l }
• H _ { 0 } : \mu \geq 48 ^ { \circ } \\
• H _ { 1 } : \mu < 48 ^ { \circ }
• \end{array}\)

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Definitions:

Consequent

The outcome of a conditional statement, coming after the "if" clause.

Disjunctive Premise

A logical statement composed of two or more propositions joined by the word "or," indicating alternatives.

Conclusion

The final statement in a logical argument or reasoning process, derived from the premises.

Hypothetical Proposition

A hypothetical proposition is a conditional statement proposing a possible scenario and its outcome, often structured in an if-then format.