Final answer:
The correct hypotheses for a significance test regarding the pizza shop's delivery promise are H₀: µ ≤ 30 (population mean delivery time is 30 minutes or less), and Hₐ: µ > 30 (population mean delivery time is greater than 30 minutes), reflecting the shop's claim and the opposite town residents' belief, respectively.
Step-by-step explanation:
To set up hypotheses for a significance test regarding the pizza shop's delivery time, first, we establish what the claim is about. In this case, the pizza shop states they deliver in 30 minutes or less. People on the opposite side of town believe it takes longer. Thus, the null hypothesis (H₀) should reflect the status quo or the claim that's being tested, which is the delivery time being 30 minutes or less. The alternative hypothesis (Hₐ) is what the residents believe, that the delivery would take more than 30 minutes.
The correct set up for the hypotheses is:
- Null Hypothesis, H₀: μ ≤ 30 minutes (The population mean delivery time is 30 minutes or less.)
- Alternative Hypothesis, Hₐ: μ > 30 minutes (The population mean delivery time is greater than 30 minutes.)
Therefore, the answer translates to option (a): H₀: μ ≤ 30, Hₐ: μ > 30. This is because we start with the assumption that the pizza shop's claim is correct, and we want to test if there's enough evidence to support the belief that it's not, which would be suggesting that the mean delivery time is greater than 30 minutes.