Question

9. The following table gives the alcohol content percentage and calories for a random sample of nine different beer brands: Alcohol 14.7 6.7 8.1 4.15 5. 1 5 547 62 Content Calories 163 215 222 104 162 158 155 158 195 a) Conduct a hypothesis test to determine if the two variables are linearly correlated. If they are, give the type of correlation (e.g. strong negative). b) Estimate alcohol content of a beer that has 170 calories. c) If a beer has a higher alcohol content than another, will it have more calories?

Answer 1

To test - Ho: P = 0 Ho : (no significant Hi I Significant V5 Hi P70 linear correlation) linear correlation) Correlation coefficient =r=10.9134) A4 0.9134 1-60-9134)? 19-2 W n-2 t - 5.9367) ta, n-2 = 2.3646 pvalue = 0.0006 As t = 5.9367] > t critical value 12.3646 so ! - We reject Ho. Conclusion - Hence, we say that two variably as linearly correlated. As r=0.913 which implies that the correlation is strong positive) ) û = 0.1201 + (0.0317) X ir xC calories) = 170 then Estimale alcohol content = 0.1201 + (0.0317) (170) 2 5.5091 e) Yes, As value of Wesay that another the value of x (varicable incrose) y variable increase from the data if beer hos higher alcohol than it have more calories.