Deck 26: Multifactor Analysis of Variance

Question 1

A student runs an experiment to study the effect that a teacher has based on the size of their class.She uses 3 different teachers on 5 different class sizes.

Answer 1

H0: γ1 = γ2 = γ3,where γ represents the effect of the teacher vs.HA: Not all of the teachers have the same effect. H0: τ1 = τ2 = τ3 = τ4 = τ5,where τ represents the effect of class size vs.HA: Not all of the class sizes have the same effect.

Question 2

The following ANOVA table shows the results of an experiment used to test scores for males and females at 4 different times of day.Assuming no effect from the interaction between gender and test time,test the claim that males and females perform the same on the test.

Answer 2

H0: γ1 = γ2,where γ represents the effect of gender vs.HA: Both genders do not have the same effect.The null hypothesis states that gender has no effect on test score.The alternative states that it does.The P-value for gender is 0.4745,which provides insufficient evidence to indicate that gender had an effect on the mean score.

Question 3

A student runs an experiment to study the effect that a teacher has based on the size of their class.She uses 3 different teachers on 6 different class sizes.

A)Teacher SS: 3 df; Class size SS: 5 df; SSE: 10 df
B)Teacher SS: 2 df; Class size SS: 5 df; SSE: 11 df
C)Teacher SS: 2 df; Class size SS: 8 df; SSE: 11 df
D)Teacher SS: 2 df; Class size SS: 5 df; SSE: 10 df
E)Teacher SS: 3 df; Class size SS: 4 df; SSE: 12 df

Answer 3

Teacher SS: 2 df; Class size SS: 5 df; SSE: 10 df

Question 4

The following ANOVA table shows the results of an experiment used to test how race car drivers and different tracks affect time.The experiment used 3 different drivers on 4 different tracks.Assuming no effect from the interaction between driver and track,test the claim that the track has no effect on time.

Question 5

The following ANOVA table shows the results of an experiment used to test the effect of car type and gas brand on mileage.In the experiment 4 different types of cars and 3 different brands of gas were used.Assuming no effect from the interaction between car and brand of gas,test the claim that the three brands of gas provide the same mean gas mileage.

Question 6

A student runs a two-factor experiment to test how toaster level and speed affect the level of crispness of a bagel.He chooses 3 levels of crispness (light,medium,dark)and 3 speeds (1 min,2 min,3 min),toasting one bagel at each condition.

A)Crispness SS: 2 df; Speed SS: 2 df; SSE: 5 df
B)Crispness SS: 2 df; Speed SS: 2 df; SSE: 4 df
C)Crispness SS: 3 df; Speed SS: 3 df; SSE: 6 df
D)Crispness SS: 2 df; Speed SS: 2 df; SSE: 6 df
E)Crispness SS: 3 df; Speed SS: 3 df; SSE: 9 df

Question 7

A student runs an experiment to test how race car drivers and different tracks affect time.He uses 3 different drivers on 4 different tracks.He randomizes the trials,performing 4 runs under each treatment condition,carefully recording how many laps each driver completes on each different track.

Question 8

The following ANOVA table shows the results of an experiment used to test the effect of car type and gas brand on mileage.In the experiment 4 different types of cars and 3 different brands of gas were used.Assuming no effect from the interaction between car and brand of gas,test the claim that the four cars have the same mean mileage.

Question 9

A student runs a two-factor experiment to test how toaster level and speed affect the level of crispness of a bagel.He chooses 3 levels of crispness (light,medium,dark)and 3 speeds (1 min,2 min,3 min),toasting one bagel at each condition.

Question 10

The following ANOVA table shows the results of an experiment used to test scores for males and females at 4 different times of day.Assuming no effect from the interaction between gender and test time,test the claim that time of day does not affect test scores.

Question 11

The following data show annual income,in thousands of dollars,categorized according to the two factors of gender and level of education.Test the null hypothesis of no interaction between gender and level of education at a significance level of 0.05.

Question 12

The following ANOVA table shows the results of a study in which three different teachers taught calculus classes of five different sizes.The class average was recorded for each class.Assuming no effect from the interaction between teacher and class size,test the claim that the teacher has no effect on the class average.

Question 13

A student runs an experiment on test scores for males and females at different times of day.She uses 4 different times of day.

A)Gender SS: 1 df; Time SS: 3 df; SSE: 3 df
B)Gender SS: 1 df; Time SS: 4 df; SSE: 4 df
C)Gender SS: 2 df; Time SS: 3 df; SSE 3 df
D)Gender SS: 1 df; Time SS: 3 df; SSE: 8 df
E)Gender SS: 2 df; Time SS: 4 df; SSE: 8 df

Question 14

A student runs an experiment to study the effect of gas brand and car type on mileage.She uses 3 different brands of gas on 4 different types of cars.

Question 15

A student runs an experiment to study the effect of gas brand and car type on mileage.She uses 3 different brands of gas on 8 different types of cars.

A)Gas brand SS: 3 df; Car type SS: 7 df; SSE: 14 df
B)Gas brand SS: 3 df; Car type SS: 4 df; SSE: 12 df
C)Gas brand SS: 1 df; Car type SS: 7 df; SSE 14 df
D)Gas brand SS: 2 df; Car type SS: 3 df; SSE: 8 df
E)Gas brand SS: 2 df; Car type SS: 7 df; SSE 14 df

Question 16

The following ANOVA table shows the results of a study in which three different teachers taught calculus classes of five different sizes.The class average was recorded for each class.Assuming no effect from the interaction between teacher and class size,test the claim that the teacher has no effect on the class average.

Question 17

The following ANOVA table shows the results of an experiment used to test how race car drivers and different tracks affect time.The experiment used 3 different drivers on 4 different tracks.Assuming no effect from the interaction between driver and track,test the claim that the three drivers have the same mean time.

Question 18

The following data shows annual income,in thousands of dollars,categorized according to the two factors of gender and level of education.Assume that incomes are not affected by an interaction between gender and level of education,and test the null hypothesis that gender has no effect on income and that level of education has no effect on income.Use a 0.05 significance level.

Question 19

A student runs an experiment on test scores for males and females at different times of day.She uses 4 different times of day.

Question 20

A student runs an experiment to test how race car drivers and different tracks affect time.He uses 3 different drivers on 4 different tracks.He randomizes the trials,performing 4 runs under each treatment condition,carefully recording how many laps each driver completes on each different track.

A)Driver SS: 2 df; Track SS: 3 df; SSE: 42 df
B)Driver SS: 3 df; Track SS: 4 df; SSE: 12 df
C)Driver SS: 3 df; Track SS: 3 df; SSE: 42 df
D)Driver SS: 2 df; Track SS: 3 df; SSE: 12 df
E)Driver SS: 3 df; Track SS: 4 df; SSE: 42 df

Question 21

The following data shows the yield,in bushels per acre,categorized according to three varieties of corn and three different soil conditions (Plot 1,Plot 2,and Plot 3).Test the null hypothesis of no interaction between variety and soil conditions at a significance level of 0.05.

Question 22

The following data shows the yield,in bushels per acre,categorized according to three varieties of corn and three different soil conditions (Plot 1,Plot 2,and Plot 3).Assume that yields are not affected by an interaction between variety and soil conditions,and test the null hypothesis that variety has no effect on yield and that soil conditions have no effect on yield.Use a 0.05 significance level.