Problem 1: ( One Way ANOVA)

The following data set lists the sales resulting from the use of three different sales methods. We want to determine if the three sales methods result in the same average sales volume.

1. Assume that all of the assumptions of ANOVA are met and use MINTAB to determine if there is a significant difference in the average sales volume among the three sales methods. \((\alpha=.05)\)
2. If necessary, perform Fisher's test to determine which of the methods differ in average sales volume. \((\alpha=.05)\)

Problem 2: (Randomized block design ANOVA)

A taste-testing experiment has been designed so that four brands of Colombian coffee are to be rated by nine experts. To avoid any carryover effects, the tasting sequence for the four brews is randomly determined for each of the nine expert tasters until a rating on a 7-point scale ( 1= extremely unpleasing. 7 = extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following table displays the ratings accumulated over all four characteristics.

1. Assume that all of the assumptions of ANOVA are met and use MINITAB to determine if there is a significant difference in the in the ratings among the experts of Columbian coffee \((\alpha=.05)\).
2. Assume that all of the assumptions of ANOVA are met and use MINITAB to determine if there is a significant difference in the ratings among the four brands of Columbian coffee \((\alpha=.05)\). If so, which brands ratings do significantly differ?

Problem 3: ( Two Way ANOVA – Full factorial design)

The quality control director for a clothing manufacturer wants to study the effect of operators and machines on the breaking strength (in pounds) of wool serge material. A batch of the material is cut into square-yard pieces and these are randomly assigned, 3 each, to all 12 combinations of 4 operators and 3 machines chosen specifically for the experiment. The results are as follows:

At the .05 level of significance:

1. Is there an interaction due to operator and machine?
2. Is there an effect due to operator?
3. Is there an effect due to machine?

Problem 4: (Simple Linear Regression)

A mail-order catalog business selling personal computer supplies, software and hardware maintains a centralized warehouse for the distribution of products ordered. Management is currently examining the process of distribution from the warehouse and is interested in studying the factors that affect warehouse distribution costs. Currently a small handling fee is added to the order, regardless of the amount of the order. Data have been collected over the past 24 months indicating the warehouse distribution costs and the number of orders received. The results are as follows:

1. Draw the scatter diagram and comment on the nature of the relationship between distribution costs and the number of orders.
2. Assume a linear relationship, use the computer software and determine the least squares linear regression equation.
3. Provide a managerial interpretation of the regression coefficients determined in part b.
4. At a significance level of .05 test the simple linear regression equation for significance.
5. Predict the average monthly warehouse distribution costs when the number of orders is 4500 and 5,500 .
6. Based on the results provided by the software package, state the value of the coefficient of determination and the standard error of estimate and interpret their meanings.
7. Use the software package and draw the residuals vs. the number of orders.
8. Use the software package and draw the residuals vs. the time period.
9. Based on the diagrams of part $f$ and $g$ comment on how well the model meets the assumptions of the simple linear regression model.
10. Use the software package and determine the Durbin-Watson statistic. At the .o5 level of significance is there evidence of positive autocorrelation among the residuals?
11. Would you recommend using this model to predict the monthly distribution costs? Why?

Problem 5: (Multiple Linear Regression)

Regina Monson, analyst for the Professional Investment Group, has been assigned the task of investigating the earnings per share for large corporations. Regina decides to collect data from Fortune 500 , a publication that lists the 500 largest industrial corporations ranked by sales. She takes a random sample of 30 corporations and records data for the following potential predictor variables: sales, profits, assets, and stockholders' equity. The data are given below:

1. Using MINITAB determine the multiple regression model based on all of the candidate variables. Interpret the meaning of all coefficients.
2. At .05 level of significance test the overall model and the individual regression coefficients for significance.
3. Calculate the value of critical \(r\) and use MINITAB to obtain the appropriate VIF values. Is there evidence of significant multicollinearity in this model? If there is multicollinearity, eliminate it and determine the best model without multicollinearity.

Price: $31.06

Solution: The downloadable solution consists of 17 pages, 1406 words and 24 charts.
Deliverable: Word Document