# Question: A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using four different designs.

Question: A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using four different designs. Ten balls were manufactured with each design and were brought to the local golf course for the club professional to test. The order in which the balls were hit with the same club from the first tee was randomized so that the pro did not know which type of ball was being hit. All 40 balls were hit in a short period of time, during which the environmental conditions were essentially the same. The results (distance traveled in yards) for the four designs are as follows, answer the following questions. Assume all balls produced in four different designs are normally distributed and balls were selected randomly and independently.

MAIN QUESTIONS

1. At the .05 level of significance, is it appropriate to perform an ANOVA test? Give your justification.

2. At the .05 level of significance, is there evidence of a difference in the mean distances traveled by the golf balls with different designs?

3. If the results in 1 indicate there is statistical significant differences on mean distances traveled by the golf balls with different designs, what designs differ in mean distances?

4. What golf ball design should the manufacturing manager choose?

DATA

Referring Quiz 2, in order to check if ANOVA is an appropriate tool to analyze this data, assumptions of ANOVA have to be satisfied. Which of following is NOT an ANOVA assumption?

Select one:

a. Populations at each group are normally distributed

b. Populations at each group should have equal variances

c. Random and Independent Sample

d. Populations at each group should have equal mean

At the level of .05, to check populations equal variances, what test do we need to perform?

Select one:

a. ANOVA test

b. Levene’s Test

c. Two-Sample F test

d. Tukey-Cramer Procedure Test

By referring question 2’s test, what is the H0 of your hypothesis?

Select one:

a. Mu1=Mu2=…=Mu10

b. Mu1=Mu2=Mu3=Mu4

c. Sigma1^2=Sigma2^2=Sigma3^2=Sigma4^2

d. Sigma1^2=Sigma2^2=…=Sigma10^2

By referring question 2’s test, what is the Test-Statistics?

Select one:

a. 2.8663

b. 13.5456

c. 6.4712

d. 2.0932

By referring Question 2’s test, what is p-value of the test?

Select one:

a. .11828

b. 2.7

c. 0

d. .04238

By referring question 5’s result, what conclusion can you draw from?

Select one:

a. Population Variations for each group are same, we cannot perform ANOVA analysis on this data

b. Population Variations for each group are same, we can perform ANOVA analysis on this data

c. Population Variations for each group are different, we can perform ANOVA analysis on this data

d. Population Variations for each group are different, we cannot perform ANOVA analysis on this data

At the .05 level of significance, to test any difference in the mean distances traveled by the golf balls with different designs, what kind of test do you plan to perform?

Select one:

a. Levene’s Test

b. ANOVA analysis

c. Two sample variance F test

d. Tukey-Cramer Procedure Test

By referring question 7’s test, what is H0 of the hypothesis?

Select one:

a. Not all Sigma are same

b. Not all Muj are same

c. Mu1=Mu2=Mu3=Mu4

d. sigma1=sigma2=sigma3=sigma4

By referring question 7’s test, what is the test-statistics of that test?

Select one:

a. 2.8663

b. 18.8007

c. 53.0298

d. 996.997

By Referring Question 7’s test, what is the p-value of the test?

Select one:

a. .0214

b. 2.7

c. .11828

d. 0

By referring question 10’s result, what conclusions can you draw from?

Select one:

a. The mean distances of all designs are same, we should go further to investigate which design is different

b. The mean distances of all designs are same, there is no further information that can be provided.

c. The mean distances of all designs are different, there is no further information that can be provided.

d. The mean distances of all designs are different, we should go further to investigate which design is different

By referring the quiz 2 problem, in order to find which design can produce significantly different distances, what test to perform?

Select one:

a. Levene’s Test

b. Tukey-Cramer Procedure test

c. ANOVA analysis

d. Brown-Forsythe Test

Suppose you plan to take Tukey-Cramer Procedure, to calculate Critical Range,what is the value of Qu in this data?

Select one:

a. 3.82

b. 3.84

c. 3.79

d. 3.77

In this data, in order to perform a Tukey-Procedure, how many pair-wise comparisons do you need to perform?

Select one:

a. 6

b. 3

c. 4

d. 5

To perform a Tukey-Cramer procedure, critical range is needed to make a decision. In this given data, how many different critical ranges do you actually need to calculate?

Select one:

a. 5

b. 2

c. 3

d. 1

To perform a Tukey-Cramer procedure, what is the value of critical range for this data?

Select one:

a. 9.6874

b. 8.6654

c. 5.19668

d. 6.2879

To perform a Tukey-Cramer procedure, what is absolute value mean difference between design 1 and design 4?

Select one:

a. 11.902

b. 22.008

c. 19.994

d. 10.106

When comparing Design 1 and Design 3, is there any evidence to show significant mean difference between two designs?

Select one:

True

False

When comparing Design 3 and Design 4, is there any evidence to show significant mean difference between two designs?

Select one:

True

False