Exam 25: Analysis of Variance

A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.Calculate MST,MSE,and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value Compound 491.207 Error 2888.847 Total 4380.054

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.The F-value from an ANOVA is 10.866.What is the P-value?

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value WireType 293.745 Error 1456.131 Total 1749.876

A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy and waiting fifteen minutes.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.

A consumer interest group is interested in comparing the speed of four different desktop printers; four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

The Professional Golfers' Association (PGA)wants to know which brand of golf ball goes the farthest when hit by a driver.Three brands of golf balls are compared by using "Iron Byron" to randomly hit each brand of ball five times.The total distance in yards is measured after each ball comes to rest.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value Brand 1405.375 Error 1467.556 Total 2872.931

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.After collecting the data and analyzing the results,she reports that the F-ratio is 1.076.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value Catalyst 9.310 Error 79.320 Total 88.630

A consumer interest group is interested in comparing the speed of four different desktop printers; four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value Printer 4.862 Error 3.150 Total 8.012

A consumer interest group is interested in comparing the speed of four different desktop printers; four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.

An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.The box plots for the three methods are shown below.

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P-value Employee 4359.540 Error 875.978 Total 5235.518

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.The box plots for the four wire types are shown below.

An independent research firm conducts a study to compare the taste of four new sports drinks.Five people are randomly assigned to each of the four drinks.Each person tastes the drink and judges it on a scale from one to five.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.