Final answer:
For a hypothesis test where the alternative hypothesis has a not-equals symbol, it is classified as a two-tailed test. In the scenario with the brewery owner testing the true mean temperature, since the alternative hypothesis is that the mean is not equal to 51 degrees, it is indeed a two-tailed test.
Step-by-step explanation:
When conducting a hypothesis test, we classify the test as left-tailed, right-tailed, or two-tailed based on the nature of the alternative hypothesis (Ha). If the alternative hypothesis has a not-equals symbol (≠), it indicates a two-tailed test. This means that we are looking for evidence that the true mean is different from the specified value, either higher or lower.
In the scenario described, where a brewery owner is testing whether the true mean temperature of refrigerators differs from 51 degrees Fahrenheit, the null hypothesis (H_o) would be that the mean temperature is equal to 51 degrees, and the alternative hypothesis (Ha) would be that the mean temperature is not equal to 51 degrees. Since Ha includes the not equals symbol, this would be a two-tailed test.
The p-value represents the probability of observing a sample statistic as extreme as the test statistic, under the assumption that the null hypothesis is true. A small p-value (< 0.05) provides evidence against the null hypothesis, leading to its rejection, while a large p-value (> 0.05) suggests that the null hypothesis should not be rejected.