Using the data below, find: (10 pts) Design1 Design2 Design3 Design4 206.32 217.
ID: 3228910 • Letter: U
Question
Using the data below, find: (10 pts)
Design1
Design2
Design3
Design4
206.32
217.08
226.77
230.55
207.94
221.43
224.79
227.95
206.19
218.04
229.75
231.84
204.45
224.13
228.51
224.87
209.65
211.82
221.44
229.49
203.81
213.90
223.85
231.10
206.75
221.28
223.97
221.53
205.68
229.43
234.30
235.45
204.49
213.54
219.50
228.35
210.86
214.51
233.00
225.09
a. What is an appropriate null hypothesis for the test for no differences in the population
means?
b. What is an appropriate alternate hypothesis?
c. What is the Q statistic?
d. What is the value of the test statistic (F)?
e. What is the critical value?
f. What is the p value?
g. At a 95% confidence level, what is your conclusion concerning the null
hypothesis? Reject / Not Reject?
h. Using the Critical Value Test, explain your conclusion concerning the null hypothesis?
i. Using the p value test, explain your conclusion concerning the null hypothesis?
j. Would a Tukey-Kramer test for multiple comparisons be appropriate? Yes / No?
Design1
Design2
Design3
Design4
206.32
217.08
226.77
230.55
207.94
221.43
224.79
227.95
206.19
218.04
229.75
231.84
204.45
224.13
228.51
224.87
209.65
211.82
221.44
229.49
203.81
213.90
223.85
231.10
206.75
221.28
223.97
221.53
205.68
229.43
234.30
235.45
204.49
213.54
219.50
228.35
210.86
214.51
233.00
225.09
Explanation / Answer
a. What is an appropriate null hypothesis for the test for no differences in the population means?
H0 : There is no difference in mean value for the given four designs. 1 =2 =3 =4
b. What is an appropriate alternate hypothesis?
Ha : There is significant difference in mean values for the given four desgns.
c. What is the Q statistic?
q = (ymax - ymin)/Sqrt [ MSE/n]
Here ymax is the maximum mean which is here for design 4 and equal to 228.62
and ymin is the minimum mean which is here for deign 1 and equal to 206.61
and n = number per treatment per group. = 10 here
q = (228.62 - 206.61)/ sqrt (18.80/10) = 16.045
d. What is the value of the test statistic (F)?
ANOVA table is attached here
Here F = 53.03
e. What is the critical value?
Fcritical = 2.87
f. What is the p value?
p - value = 0.00
g. At a 95% confidence level, what is your conclusion concerning the null
hypothesis? Reject / Not Reject?
Reject null hypothesis as F > Fcritical
h. Using the Critical Value Test, explain your conclusion concerning the null hypothesis?
We conclude that there is significant difference between means of various desing.
i. Using the p value test, explain your conclusion concerning the null hypothesis?
Yes, there is significant difference in means and we can reject the null hypothesis
j. Would a Tukey-Kramer test for multiple comparisons be appropriate?
Yes / No?
Yes , tukey - kramer test is also appropriate for multiple comparisons.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Design1 10 2066.14 206.614 5.246427 Design2 10 2185.16 218.516 30.66718 Design3 10 2265.88 226.588 23.18213 Design4 10 2286.22 228.622 16.10697 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2990.99 3 996.9966 53.02982 2.73E-13 2.866266 Within Groups 676.8244 36 18.80068 Total 3667.814 39Related Questions
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