Question

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ​( mu μ​, ​p, sigma 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, mu μ​, of 48 degrees °​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.

Answer 1

Null hypothesis:
`H_0:\; \mu = 48\; ^\circ\rm F`.

Alternative hypothesis:
`H_1:\; \mu \\e 48\; \rm ^\circ F`.

Explanation:

In hypothesis testing, the alternative hypothesis
`H_1` represents the claim that is being tested. According to the claim in this question, the true (population) mean
`\mu` is "incorrect," or not equal to ("
`\\e`") the proposed value of
`48\; \rm ^\circ F`. Hence, the alternative hypothesis for this question would be
`H_0:\; \mu \\e 48\; \rm ^\circ F`.

On the other hand, the null hypothesis represents what happens when that claim is disproved; it should always use the equal sign ("
`=`".) In this question, that's the same as saying that the (population) mean
`\mu` is indeed equal to
`48\; \rm ^\circ F`. Hence, the null hypothesis for this question would be:
`H_1:\; \mu = 48\; \rm ^\circ F`.