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

Answer:

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

Alternative hypothesis: $H_1:\; \mu \ne 48\; \rm ^\circ F$.

Step-by-step 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 ("$\ne$") the proposed value of $48\; \rm ^\circ F$. Hence, the alternative hypothesis for this question would be $H_0:\; \mu \ne 48\; \rm ^\circ F$.

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: $H_1:\; \mu = 48\; \rm ^\circ F$.