Exam 25: Analysis of Variance

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.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

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.

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.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

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.The number of geese attracted by the decoy is counted.

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.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 Drink 25.200 Error 10.000 Total 35.200

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.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

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 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.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

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 one of 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.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

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.The F-value from an ANOVA is 6.173.What is the P-value?

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.After collecting the data and analyzing the results,he reports that the F-ratio is 3.097.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

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.The box plots for the five employees are shown below.

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 box plots for the four types of fertilizer are shown below.

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.

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.

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.The number of geese attracted by the decoy is counted.The data are analyzed and calculations show an F-ratio of 7.878.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

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.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.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 Fert 283.966 Error 174.218 Total 458.184

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.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 Method 985535.907 Error 276844.275 Total 1262380.182

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 with time as the dependent variable.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 CallBrand 8.933 Error 6.800 Total 15.733