A restaurant manager suspects that service declines during off-peak hours. To investigate, he selects a random sample of 100 customers who dined in his restaurant during peak hours and a random sample of 70 customers who dined in his restaurant during off-peak hours. Each customer rated the service on a scale of 1 to 5, where 1 = highly dissatisfied and 5 = highly satisfied. The results are displayed in the table.



The manager would like to test these hypotheses:

H0: There is no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.
Ha: There is a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.



The conditions for inference are met. The test statistic is χ‑2 = 13.88 and the P-value is between 0.005 and 0.01. What conclusion should be made using α = 0.05?

Because the P-value is less than α = 0.05, there is convincing evidence of a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.
Because the P-value is less than α = 0.05, there is convincing evidence of no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.
Because the P-value is less than α = 0.05, there is not convincing evidence of a difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.
Because the P-value is less than α = 0.05, there is not convincing evidence of no difference in the distribution of service ratings among all customers who dine at this restaurant during peak and off-peak hours.