Final answer:
The correct null hypothesis is H₀: p = 0.5, indicating no difference from 50%, and the alternative hypothesis should be H₁: p > 0.5 to reflect the belief that more than half the workers want more overtime, not H₁: p < 0.5 as mistakenly provided.
Step-by-step explanation:
To test the workers' representative's belief that more than half the workers at the factory want the opportunity to work more overtime hours, we should set up the appropriate null and alternative hypotheses. Hypothesis testing is a method used in statistics to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population.
The null hypothesis (H₀) usually states that there is no effect or no difference, and it is the hypothesis that one typically aims to challenge. In this case, the null hypothesis should be that the proportion of workers who want more overtime hours is equal to 0.5 (50%), or H₀: p = 0.5. The alternative hypothesis (H₁) should reflect the workers' representative's claim and is stated as a contradiction to the null hypothesis. Since the representative believes that more than half the workers want more overtime, the alternative hypothesis should be that the proportion of workers who want more overtime hours is greater than 0.5, or H₁: p > 0.5.
If the student's question mistakenly provided H₁: p < 0.5, correct the hypothesis to reflect the belief that more workers want overtime, which is H₁: p > 0.5. After formulating the correct hypotheses, statistical tests such as a one-tailed test can be used to analyze the data and draw conclusions about the workers' preferences for overtime hours.