Question

Designi Design2 Design3 Design4 206.32 217.08 226.77 230.55 07.94 221.43 224.79 227.95 206.19218.04 229.7 231.84 20445 22413 228.51 224.87 209.65 21182 22144 229.49 203.81 13.9 223.85 231.1 206.7522128223.7 221.53 05.68229.43 234.3 235.45 204.49 213.54 219.5 228.35 233 225.09 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 To perform a Tukey-Cramer procedure, critical range is needed to make a decision in this given data, how many To perform a Tukey-Cramer procedure, what is the value of critical range for this data? different critical ranges do you actually need to calculate? Select one: Select one 1086 21451 a. 5.19668 b. 9.6874 c. 8.6654 d. 6.2879 O a. 5 Ο O b. 2 d. 3 To perform a Tukey-Cramer procedure, what is absolute value mean difference between design 1 and design 47 Select one O a. 11.902 O b. 19.994 O c,10.106 d. 22.008

1)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?

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

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

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

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

6)What golf ball design should the manufacturing manager choose? choose one or more designs

Answer 1

Anova table

anova table
	SS	df	MS	F
Between:	2990.990	3	996.997	53.030
Within:	676.824	36	18.801
Total:	3667.814	39

Level of significance	0.01
no. of treatments,k	4
DF error =N-k=	36
MSE	18.801
q-statistic value(α,k,N-k)	3.79

	design1	design2	design3	design4
count, ni =	10	10	10	10
mean , x̅ i =	206.61	218.52	226.59	228.62

critical value = q*√(MSE/2*(1/ni+1/nj))  

1) since, all sample size are equal,so, all critical value will be same.so, number of different critical values = 1

2) critical value = q*√(MSE/2/(1/n+1/n) =  5.19668 * √(18.801/10) = 5.19668

3) µ1-µ4 = | 206.61 - 228.62 | = 22.008

4) if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
                      

absolute mean difference		critical value			result
µ1-µ3	19.974	5.19668			means are different

true , there is any evidence to show significant mean difference between two designs

5)

population mean difference		critical value			result
µ3-µ4	2.034	5.1967			means are not different

False,

there is no enough evidence to show significant mean difference between two designs.