Question

One-Way Anova

Instructions: Before answering the questions below, please watch the video recordings on Chapter 11 Hypothesis Testing Using the One-Way Analysis of Variance under 'This Week's Content'. Then open the practice problem that is attached to this discussion board. Complete the attached practice problem using what you learned in the videos and following the steps below. Upload a picture of your written out answer to the practice problem. You are required to show all work, which will include completing the following steps:

1. Determine your null and alternative hypotheses
2. Compute the following values in this particular order (i.e., following the video):
   1. Sum of squares total
   2. Sum of squares between
   3. Sum of squares within
   4. Degrees of freedom between
   5. Degrees of freedom within
   6. Degrees of freedom total
   7. Mean squares between
   8. Mean squares within
   9. F-obtained
3. Identify the f critical using the chart in the back of the book
4. Compare the f obtained to the f critical to determine if the f obtained falls within the region of rejection
5. Determine whether to accept or reject the null hypothesis
6. If you reject the null hypothesis, compute Tukey's HSD
7. Compute the difference between the means for every pairing of groups
8. Interpret Tukey's HSD by comparing the values in Step 7 to the value in Step 6. Determine which group means are significantly different from each other.

USe alpha =0.05

group 1 data

14,14,13,10,14,15

group 2 data

10,13,12,11,11,10

group 3 data

11,15,14,13,14,15

Answer 1

1)

Ho: µ1=µ2=µ3
H1: not all means are equal

2)

count, ni =	6	6	6
mean , x̅ i =	13.333	11.17	13.67
std. dev., si =	1.751	1.169	1.506
sample variances, si^2 =	3.067	1.367	2.267
total sum	80	67	82		229	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				12.72

SS(between)= SSB = Σn( x̅ - x̅̅)² =	2.241	14.519	5.352		22.11111
SS(within ) = SSW = Σ(n-1)s² =	15.333	6.833	11.333		33.5000

SST=Σ( x - x̅̅ )² =    55.611

3)

SS(between)= SSB = Σn( x̅ - x̅̅)² = 22.111

4)

SS(within ) = SSW = Σ(n-1)s² = 33.5

5)

df between = k-1 =    2

6)

N = Σn =   18
df within = N-k =   15

7)

Df total = 17

8)

mean square between groups , MSB = SSB/k-1 =    11.0556

9)
  
mean square within groups , MSW = SSW/N-k =    2.2333

10)
  
F-stat = MSB/MSW =    4.9502

11)

F-critical

3.68

12)

F > F critical

13)

Reject

	SS	df	MS	F	p-value	F-critical
Between:	22.11	2	11.06	4.95	0.0223	3.68
Within:	33.50	15	2.23
Total:	55.61	17
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

Thanks in advance!

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