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 tables. Observed counts: Expected counts: 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. 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. Which service rating contributed most to the significance of this test?
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 tables.
Observed counts:
Expected counts:
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. 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.
Which service rating contributed most to the significance of this test?
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