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Question 1 In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and White Castle. Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on the basis of taste, and then ranked the restaurants from 1 through 6 on the basis of overall preference. In each case, 1 is the best rating and 6 the worst. The mean ratings given by the 406 individuals are given in the following table: Mean Mean Taste Restaurant Preference Borden Burger 3.5659 4.2552 Hardee's 3.329 4.0911 Burger King 2.4231 3.0052 McDonald's 2.0895 2.2429 Wendy's 1.9661 2.5351 White Castle 3.8061 4.7812 Figure 14.16 gives the Excel output of a simple linear regression analysis of this data. Here, mean preference is the dependent variable and mean taste is the independent variable. Recall that a labeled Excel regression output is given on page 505. a Find the least squares point estimate b, of ß, on the computer output. Report and interpret this estimate. b Find the 95 percent confidence interval for B, on the output. Report and interpret the interval. FIGURE 14.16 Excel Output of a Simple Linear Regression Analysis of the Fast-Food Restaurant Rating Data Regression Statistics Multiple R 0.9873 R Square 0.9747 Adjusted R Square 0.9684 Standard Error 0.1833 Observations 6 ANOVA df SS Significance F MS 5.1817 F 154.2792 Regression 1 5.1817 0.0002 Residual 0.1343 0.0336 Total 5.3160 Standard Error t Stat Lower 95% P-value 0.6248 Intercept 0.3029 -0.5289 -1.0011 MeanTaste (x) 0.1025 12.4209 0.0002 0.9885 4 5 Coefficients -0.1602 1.2731 Upper 95% 0.6807 1.5577

Question 1 In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and White Castle. Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on the basis of taste, and then ranked the restaurants from 1 through 6 on the basis of overall preference. In each case, 1 is the best rating and 6 the worst. The mean ratings given by the 406 individuals are given in the following table: Mean Mean Taste Restaurant Preference Borden Burger 3.5659 4.2552 Hardee's 3.329 4.0911 Burger King 2.4231 3.0052 McDonald's 2.0895 2.2429 Wendy's 1.9661 2.5351 White Castle 3.8061 4.7812 Figure 14.16 gives the Excel output of a simple linear regression analysis of this data. Here, mean preference is the dependent variable and mean taste is the independent variable. Recall that a labeled Excel regression output is given on page 505. a Find the least squares point estimate b, of ß, on the computer output. Report and interpret this estimate. b Find the 95 percent confidence interval for B, on the output. Report and interpret the interval. FIGURE 14.16 Excel Output of a Simple Linear Regression Analysis of the Fast-Food Restaurant Rating Data Regression Statistics Multiple R 0.9873 R Square 0.9747 Adjusted R Square 0.9684 Standard Error 0.1833 Observations 6 ANOVA df SS Significance F MS 5.1817 F 154.2792 Regression 1 5.1817 0.0002 Residual 0.1343 0.0336 Total 5.3160 Standard Error t Stat Lower 95% P-value 0.6248 Intercept 0.3029 -0.5289 -1.0011 MeanTaste (x) 0.1025 12.4209 0.0002 0.9885 4 5 Coefficients -0.1602 1.2731 Upper 95% 0.6807 1.5577

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question 1 In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and White Castle. Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on the basis of taste, and then ranked the restaurants from 1 through 6 on the basis of overall preference. In each case, 1 is the best rating and 6 the worst. The mean ratings given by the 406 individuals are given in the following table: Mean Mean Taste Restaurant Preference Borden Burger 3.5659 4.2552 Hardee's 3.329 4.0911 Burger King 2.4231 3.0052 McDonald's 2.0895 2.2429 Wendy's 1.9661 2.5351 White Castle 3.8061 4.7812 Figure 14.16 gives the Excel output of a simple linear regression analysis of this data. Here, mean preference is the dependent variable and mean taste is the independent variable. Recall that a labeled Excel regression output is given on page 505. a Find the least squares point estimate b, of ß, on the computer output. Report and interpret this estimate. b Find the 95 percent confidence interval for B, on the output. Report and interpret the interval. FIGURE 14.16 Excel Output of a Simple Linear Regression Analysis of the Fast-Food Restaurant Rating Data Multiple R 0.9873 R Square 0.9747 Adjusted R Square 0.9684 Standard Error 0.1833 Observations 6 ANOVA df SS F Significance F MS 5.1817 Regression 1 5.1817 154.2792 0.0002 Residual 4 0.1343 0.0336 Total 5 5.3160 Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.1602 0.3029 -0.5289 0.6248 -1.0011 MeanTaste (x) 1.2731 0.1025 12.4209 0.0002 0.9885 Regression Statistics Upper 95% 0.6807 1.5577
Transcribed Image Text:Question 1 In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and White Castle. Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on the basis of taste, and then ranked the restaurants from 1 through 6 on the basis of overall preference. In each case, 1 is the best rating and 6 the worst. The mean ratings given by the 406 individuals are given in the following table: Mean Mean Taste Restaurant Preference Borden Burger 3.5659 4.2552 Hardee's 3.329 4.0911 Burger King 2.4231 3.0052 McDonald's 2.0895 2.2429 Wendy's 1.9661 2.5351 White Castle 3.8061 4.7812 Figure 14.16 gives the Excel output of a simple linear regression analysis of this data. Here, mean preference is the dependent variable and mean taste is the independent variable. Recall that a labeled Excel regression output is given on page 505. a Find the least squares point estimate b, of ß, on the computer output. Report and interpret this estimate. b Find the 95 percent confidence interval for B, on the output. Report and interpret the interval. FIGURE 14.16 Excel Output of a Simple Linear Regression Analysis of the Fast-Food Restaurant Rating Data Multiple R 0.9873 R Square 0.9747 Adjusted R Square 0.9684 Standard Error 0.1833 Observations 6 ANOVA df SS F Significance F MS 5.1817 Regression 1 5.1817 154.2792 0.0002 Residual 4 0.1343 0.0336 Total 5 5.3160 Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.1602 0.3029 -0.5289 0.6248 -1.0011 MeanTaste (x) 1.2731 0.1025 12.4209 0.0002 0.9885 Regression Statistics Upper 95% 0.6807 1.5577
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