The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.â  Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners' overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (Let x1 represent average meal price, x2 represent type of restaurant, and y represent overall customer satisfaction.) Restaurant Type Price ($) Score
Bertucci's Italian 16 77
Black Angus Steakhouse Seafood/Steakhouse 24 79
Bonefish Grill Seafood/Steakhouse 26 85
Bravo! Cucina Italiana Italian 18 84
Buca di Beppo Italian 17 81
Bugaboo Creek Steak House Seafood/Steakhouse 18 77
Carrabba's Italian Grill Italian 23 86
Charlie Brown's Steakhouse Seafood/Steakhouse 17 75
Il Fornaio Italian 28 83
Joe's Crab Shack Seafood/Steakhouse 15 71
Johnny Carino's Italian 17 81
Lone Star Steakhouse & Saloon Seafood/Steakhouse 17 76
Longhorn Steakhouse Seafood/Steakhouse 19 81
Maggiano's Little Italy Italian 22 83
McGrath's Fish House Seafood/Steakhouse 16 81
Olive Garden Italian 19 81
Outback Steakhouse Seafood/Steakhouse 20 80
Red Lobster Seafood/Steakhouse 18 78
Romano's Macaroni Grill Italian 18 82
The Old Spaghetti Factory Italian 12 79
Uno Chicago Grill Italian 16 76
(a) Develop the estimated regression equation to show how overall customer satisfaction is related to the independent variable average meal price. (Round your numerical values to two decimal places.)
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(b) At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between overall customer satisfaction and average meal price. (Use an F test.)
State the null and alternative hypotheses.
H0: β1 ⥠0
Ha: β1 < 0H0: β1 ⤠0
Ha: β1 > 0 H0: β1 = 0
Ha: β1 > 0H0: β1 = 0
Ha: β1 â  0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship. Reject H0. There is sufficient evidence to conclude that there is a significant relationship. Reject H0. There is insufficient evidence to conclude that there is a significant relationship. Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship.
(c) Develop a dummy variable that will account for the type of restaurant (Italian or seafood/steakhouse).
Let x2 = 0 if the restaurant is an Italian restaurant and x2 = 0 if the restaurant is a seafood/steakhouse. Let x2 = 1 if the restaurant is an Italian restaurant and x2 = 1 if the restaurant is a seafood/steakhouse. Let x2 = 1 if the restaurant is an Italian restaurant and x2 = 0 if the restaurant is a seafood/steakhouse.
(d) Develop the estimated regression equation to show how overall customer satisfaction is related to the average meal price and the type of restaurant. (Use the dummy variable developed in part (c). Round your numerical values to two decimal places.)
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(e) Is type of restaurant a significant factor in overall customer satisfaction? (Use α = 0.05.)
State the null and alternative hypotheses.
H0: β2 = 0
Ha: β2 > 0H0: β2 = 0
Ha: β2 â  0 H0: β2 ⤠0
Ha: β2 > 0H0: β2 ⥠0
Ha: β2 < 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude that the type of restaurant is a significant factor. Do not reject H0. There is sufficient evidence to conclude that the type of restaurant is a significant factor. Reject H0. There is sufficient evidence to conclude that the type of restaurant is a significant factor. Reject H0. There is insufficient evidence to conclude that the type of restaurant is a significant factor.
(f) Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $15. (Round your answer to two decimal places.)
How much would the predicted score have changed for an Italian restaurant? (Round your answer to two decimal places.)
The predicted satisfaction score increases by points for Italian restaurants.