Business Statistics II - A candy bar manufacturer is interested

Business Statistics II Questions

1. (30 pts) A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. (SSTotal = 6294 and SSE = 844)

 

City Price ($) # candy bars sold

Solebury 1.30 100

Monmouth 1.40 90

Royston 1.50 90

Decatur 1.60 40

Athens 1.70 38

Colbert 1.80 32

 

a) Draw a scatter diagram with the estimated regression line.

b) Enter the data into your calculator and determine the regression line

c) Interpret the slope, b1

d) Calculate the coefficient of determination, r2, and interpret.

e) Calculate correlation coefficient, r , and interpret.

f) If the price of the candy bar is set at $1.55, what is the predicted sales?

g) At the 0.05 level of significance, is there evidence of a linear relationship between the cost of the candy bar and number of candy bars sold? (perform an F-test)

 

2. (30 pts) y = height of California redwood tree (feet)

x1 = diameter of the tree four feet off the ground (feet)

x2 = thickness of the bark(inches)

b0 = 62.14

b1 = 2.06

b2 = 10.84

 

a) Determine the regression equation and predict the height of a California redwood tree if the diameter of the tree is 18 feet and the bark is 5 inches thick.

b) Interpret the slope b1.

c) Calculate and interpret the adjusted coefficient of determination, R-Sq-adj.

d) Is there a significant relationship between the height of the California redwoods and the two independent variables, diameter and bark thickness, at the 0.05 level of significance?

Source	SS	df	MS	F
regression	25.04
error
total	59.18	20

 

e) Determine whether each independent variable makes a significant contribution to the regression model. Indicate the independent variables to include in this model. alpha = 0.05, Sb1 = 0.44, Sb2 = 6.03

 

3. (10 pts) To study the effect of temperature on yield in a chemical process, five replicates were performed at each of three temperature levels. Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. SSTreatment = 70, SSError = 236.

 

4. (10 pts) In a recent wine tasting at a restaurant, seven people rated five wines. They had no knowledge of the country of origin or the price of each wine. The restaurant owners wanted to determine if there was a difference among the five wines in terms of taste. Is there evidence of a difference among the wines at alpha = 0.05? SSTreatment = 15.12, SSBlock = 40.60, SSError = 30.09

 

5. (10 pts) A hotel wants to develop a new system for delivering room service breakfasts. The factors included were the menu choice (fruit platter, hot meal, or cold cereal) and the desired time period in which the order was to be delivered (6am, 8am, or 10am). Is there a significant effect due to the menu choice? Is there a significant effect due to time period? alpha = 0.05, SS(menu choice) = 55.46, SS(time period) = 13.11, SS(interaction) = 5.40, SS(error) = 44.37, nT = 27

 

6. (10 pts) Is there a difference in the average number of defects recorded from three different machines? To investigate this, defects were recorded for ten days for each machine, and the averages are shown below. An F test showed there was significant evidence of a difference between the average number of defects per day and the three machines.

 

Machine Ave # defects/day $ cost of new machine

Machine 1 10.1 $450,000

Machine 2 8.4 $460,000

Machine 3 14.6 $452,000

 

a. Use the Fisher LSD method to determine which machine is different. Use MSE = 5.67 and alpha = 0.05

 

b. If the company wants to buy a new machine that will save money and produce low defects, which machine should they buy? Why?