**Instructions:** Please print out and complete the following assignment writing your answers clearly and showing your work directly on the assignment. Follow directions carefully (underlining or circling your answers). Be sure to turn the assignment in at the __beginning of class on Tuesday, February 7th__. Late homeworks cannot be accepted.

*(These first two questions refer to homework problems from Homework #1):*

- The Sweet Baby Ray’s barbecue sauce factory uses a machine to put 16 ounces of its sauce into each container. After using the machine for many years, the Sweet Baby Ray’s company knows that the amount of product in each container follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.15 ounce. A sample of 50 containers filled last hour revealed that the mean amount per container was 16.017 ounces. Does this evidence suggest that the mean amount dispensed is different from 16 ounces? Use the .05 significant level.
- a) Calculate the p-value for this hypothesis test. Draw a picture of what this looks like: (4 points)

- b) What decision do you make regarding the null hypothesis? Based on what you just found, why is this so? (2 points)

- The mean life of an Energizer battery used in a calculator is 305 days. The lives of batteries follow the normal distribution. The battery was recently modified to last longer. A sample of 20 of the new batteries had a mean life of 311 days with a standard deviation of 12 days. Did the modification increase the mean life of the battery? Use the .05 significance level.
- a) Calculate the (approximate) p-value for this hypothesis test. Draw a picture of what this looks like: (4 points)

- b) What decision do you make regarding the null hypothesis? Based on what you just found, why is this so? (2 points)

- The California Department of Transportation is looking at the connection between the number of potential road builders on a highway project and the winning (or the lowest) bid for the project. Specifically, they would like to know if the number of bidders increases or decreases the amount of the winning bid. The data from this study can be found on Canvas under the file: Bidders.xlsx.

- a) Determine the regression equation. Calculate using the approach shown in class—either by hand or in Excel. (If you use Excel, please attach a printout of your spreadsheet and highlight the numbers that you plug into the formulas). (4 points)

- b) Do more bidders tend to increase or decrease the amount of the winning bid? How do you know? (2 points)

- c) Estimate the amount of the winning bid if there were seven bidders (2 points):

- A pet store manager is looking at the association between the weight of a dog and its daily food consumption. The Excel file Dog.xlsx shows the data that he collected.

- a) Compute the correlation coefficient between the two variables, and interpret this value (strength and direction). Show your work. (3 points)

- b) Determine the regression equation. Calculate using the approach shown in class—either by hand or in Excel. (If you use Excel, please attach a printout of your spreadsheet and highlight the numbers that you plug into the formulas). (4 points)

- c) How much does each additional cup of food change the weight of a dog? (3 points)