Question

Most restaurants offer free refills for its customers who purchase a fountain soft drink. A certain buffet restaurant currently doesn’t. But, it has been argued that customers who drink more soft drinks tend to eat less and, thus, cost the restaurant less for the meal the customer eats. To test this argument, this restaurant offered free refills to a sample of 6 of its customers. The total number of glasses each customer drank, X, and the $ cost of the meal each ate, Y, were recorded. The findings along with some additional calculations appear in the following table.

Customer x y

1 2 10 - 0.5 2 0.25 4 - 1.0

2 1 8 - 1.5 0 2.25 0 0.0

3 3 6 0.5 - 2 0.25 4 - 1.0

4 0 13 - 2.5 5 6.25 25 - 12.5

5 4 6 1.5 - 2 2.25 4 - 3.0

6 5 5 2.5 - 3 6.25 9 - 7.5

15 48 0 0 17.50 46 - 25.0

Using the above results, determine the following. (Show your work and highlight your final answers either with a highlighter or by placing a box around it. Calculate all values to 4 decimal places.) DO NOT ANSWER THE FOLLOWING PARTS BY RUNNING EXCEL’S ‘Regression’ ANALYIS TOOL.

1. The standard deviation of Y

2. The standard deviation of X

3. The correlation coefficient between X and Y

4. The slope of the regression line expressing the linear relationship between cost and number of glasses

5. The y-intercept of this regression line

6. R²

Using any of your above answers and the value of SE(b₁) = .38333, at the .05 level of significance is there sufficient evidence that the more glasses of a soft drink the customer drink, the less the total cost of the meal that a customer consumes.? When answering this question, complete the following but DO NOT ANSWER ANY OF THESE PARTS BY RUNNING EXCEL’S ‘Regression’ ANALYIS TOOL. No diagrams are necessary but may be useful in determining correct answers.

Hypotheses

Test statistic

Decision rule in terms of the value of the test statistic

p-value (use the t-table, do not use Excel, in determining the p-value)

conclusion

Answer 1