## Statistics 310 The Accompanying Table Contains A Food Critic’S

The accompanying table contains a food critic’s ratings for food, décor,service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in suburban areas outside the city. You want to study differences in the cost of a meal between restaurants in the city and suburban areas and also want to be able to predict the cost of a meal. Completely analyze the data. Test for the difference between the mean cost of a city meal and the mean cost of a suburban meal, using ? =0. 05. Choose an appropriate set of hypotheses, where ?1 is the mean cost of a meal in the city and ?2 is the mean cost of a meal in the suburbsA. Ho: µ1 = µ2 B. Ho: µ1 > µ2 H1: µ1 < µ2 H1: µ1 = µ2C: Ho: µ1 = µ2 D: H0: µ 1? µ 2 H1: µ1 ? µ 2 H1: µ 1 = µ 2The test statistic is ______The p-value is _________Make a conclusion. Because the p-value is less than/greater than ? =0. 05, reject/do not reject. There is enough/not enough evidence to conclude that the population mean cost of a city mean is different from the population mean cost of a suburban meal. To predict the cost of a meal, construct a multiple regression model. Let X1=food rating, X2 equals=decor rating, X3 =service rating, and X4=location. Determine the VIF for each independent variable. VIF for X1=VIF for X2=VIF for X3=VIF for X4=Which variable or variables, if any, should be eliminated due to multicollinearity? Note that if any variables are eliminated due to the VIFs calculated above, recalculate the VIFs for the remaining variables and continue this process (removing variables and recalculating VIFs) until no variables need to be eliminated due to multicollinearity. Select all that apply. A. X3B. X1C. X2D. X4E. No variables should be eliminatedPerform a best-subsets regression. Use the results to generate a list of models in which all variables are significant (using ?=0. 05) and that satisfies the Cp statistic criterion. Of these models, select the model that has the highest adjusted r2. Select the correct model below and fill in the answer boxes to complete your choice. A. Yi = ___ + ____X1i +_____X2i + _____ X3i + _____X4iB. Yi = _____ + ____ X1i + ______X2i + ______X3iC. Yi = _____ + _____X1i+_______X3iD. Yi= _______ + _____X1i + ______X3i + ______X4iUse the regression to address the difference between the costs of city and suburban meals. Choose the correct answer below. A. Taking the ratings into account, low-service suburban meals are significantly more expensive than high-service suburban mealsB. Taking the ratings into account, suburban meals are significantly more expensive than city meals, on average. C. Taking the ratings into account, city meals are significantly more expensive than suburban meals, on average. . D. Taking the ratings into account, there is not a significant difference between the mean costs of city and suburban meals. Food_Rating Decor_Rating Service_Rating302231152025231921191818241618222221222020201919211719201818232224201920211921241921252323222121231522262224212321241519211519231616252126222021262524232121221917262023262325242324222323241623201719251923232021211922201618231518262424211818221619192321241921231620242622Location_(0=City_1=Suburbs)Cost000000000000000000000000000000000000000000000403043324444504244366150515076534477574329347750745667576680684248603545322574433955653561212123232324221822222320192227192224192121232321242024232323192226221921262221202223242324261717191914201813231825121819211411221523191920131918221716181217272115121825212018202127241718192221192222182024241819212718192419212123221922202422212222212423172022212120221923222224000001111111111111111111111111111111111111111137544133274748355944513736435234385134513451562634344440315441507160372734483944413747676849222420262218262522221819191520272625192220232118252322111111111293339392846706052

## STATISTICS 310 The accompanying table contains a food critic’s

Question

The accompanying table contains a food critic’s ratings for food, décor,service, and cost per person for a sample of 50 restaurants located in a city and 50 restaurants located in suburban areas outside the city. You want to study differences in the cost of a meal between restaurants in the city and suburban areas and also want to be able to predict the cost of a meal. Completely analyze the data.

Test for the difference between the mean cost of a city meal and the mean cost of a suburban meal, using ? =0.05.

Choose an appropriate set of hypotheses, where ?1 is the mean cost of a meal in the city and ?2 is the mean cost of a meal in the suburbs

A. Ho: µ1 = µ2 B. Ho: µ1 > µ2

H1: µ1 < µ2 H1: µ1 = µ2 C: Ho: µ1 = µ2 D: H0: µ 1? µ 2 H1: µ1 ? µ 2 H1: µ 1 = µ 2 The test statistic is ______ The p-value is _________ Make a conclusion. Because the p-value is less than/greater than ? =0.05, reject/do not reject. There is enough/not enough evidence to conclude that the population mean cost of a city mean is different from the population mean cost of a suburban meal.To predict the cost of a meal, construct a multiple regression model. Let X1=food rating, X2 equals=decor rating, X3 =service rating, and X4=location. Determine the VIF for each independent variable. VIF for X1= VIF for X2= VIF for X3= VIF for X4= Which variable or variables, if any, should be eliminated due to multicollinearity? Note that if any variables are eliminated due to the VIFs calculated above, recalculate the VIFs for the remaining variables and continue this process (removing variables and recalculating VIFs) until no variables need to be eliminated due to multicollinearity. Select all that apply. A. X3 B. X1 C. X2 D. X4 E. No variables should be eliminated Perform a best-subsets regression. Use the results to generate a list of models in which all variables are significant (using ?=0.05) and that satisfies the Cp statistic criterion. Of these models, select the model that has the highest adjusted r2. Select the correct model below and fill in the answer boxes to complete your choice. A. Yi = ___ + ____X1i +_____X2i + _____ X3i + _____X4i B. Yi = _____ + ____ X1i + ______X2i + ______X3i C. Yi = _____ + _____X1i+_______X3i D. Yi= _______ + _____X1i + ______X3i + ______X4i Use the regression to address the difference between the costs of city and suburban meals. Choose the correct answer below. A. Taking the ratings into account, low-service suburban meals are significantly more expensive than high-service suburban meals B. Taking the ratings into account, suburban meals are significantly more expensive than city meals, on average. C. Taking the ratings into account, city meals are significantly more expensive than suburban meals, on average.. D. Taking the ratings into account, there is not a significant difference between the mean costs of city and suburban meals. Food_Rating Decor_Rating Service_Rating 30 22 31 15 20 25 23 19 21 19 18 18 24 16 18 22 22 21 22 20 20 20 19 19 21 17 19 20 18 18 23 22 24 20 19 20 21 19 21 24 19 21 25 23 23 22 21 21 23 15 22 26 22 24 21 23 21 24 15 19 21 15 19 23 16 16 25 21 26 22 20 21 26 25 24 23 21 21 22 19 17 26 20 23 26 23 25 24 23 24 22 23 23 24 16 23 20 17 19 25 19 23 23 20 21 21 19 22 20 16 18 23 15 18 26 24 24 21 18 18 22 16 19 19 23 21 24 19 21 23 16 20 24 26 22 Location_(0=City_1=Suburbs) Cost 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 30 43 32 44 44 50 42 44 36 61 50 51 50 76 53 44 77 57 43 29 34 77 50 74 56 67 57 66 80 68 42 48 60 35 45 32 25 74 43 39 55 65 35 61 21 21 23 23 23 24 22 18 22 22 23 20 19 22 27 19 22 24 19 21 21 23 23 21 24 20 24 23 23 23 19 22 26 22 19 21 26 22 21 20 22 23 24 23 24 26 17 17 19 19 14 20 18 13 23 18 25 12 18 19 21 14 11 22 15 23 19 19 20 13 19 18 22 17 16 18 12 17 27 21 15 12 18 25 21 20 18 20 21 27 24 17 18 19 22 21 19 22 22 18 20 24 24 18 19 21 27 18 19 24 19 21 21 23 22 19 22 20 24 22 21 22 22 21 24 23 17 20 22 21 21 20 22 19 23 22 22 24 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 37 54 41 33 27 47 48 35 59 44 51 37 36 43 52 34 38 51 34 51 34 51 56 26 34 34 44 40 31 54 41 50 71 60 37 27 34 48 39 44 41 37 47 67 68 49 22 24 20 26 22 18 26 25 22 22 18 19 19 15 20 27 26 25 19 22 20 23 21 18 25 23 22 1 1 1 1 1 1 1 1 1 29 33 39 39 28 46 70 60 52

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