Question

Jill is studying the weights of adult dogs and takes a random sample from 3 populations. Jill wants to know if the 3 breeds of dogs all hae the same population mean weight. She takes a random sample from each population and will do an ANOVA test

Bulldogs { 54, 58, 44, 46, 62, 60 }

Greyhounds { 68, 59, 65, 47, 71, 62 }

Keeshonds { 64, 58, 66, 52, 50 }

a.)What is Bob’s null and alternative hypothesis?

b.)Find the sample size, sample mean, and sample variance of all three samples.

c.) Find the over all sample mean

d.) Find SSA, SSE, MSA, MSE, test statisitc F. Draw ANOVA table

e.) Draw a picture of the rejection region ( alpha=0.5) on the appropriate curve and identify the critical value

f.)whats Jills conclusion

g.) what assumptions, if any, were required to complete this hypothesis test

Answer 1

a)

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

b)

treatment	A	B	C
count, ni =	6	6	5
mean , x̅ i =	54.000	62.00	58.000
std. dev., si =	7.483	8.485	7.071
sample variances, si^2 =	56.000	72.000	50.000

c) grand mean , x̅̅ =    Σni*x̅i/Σni =                 58.00

d)

treatment	A	B	C
SS(between)= SSB = Σn( x̅ - x̅̅)² =	96.000	96.000	0.000		192
SS(within ) = SSW = Σ(n-1)s² =	280.000	360.000	200.000		840.0000

SSA=192

SSE=840

mean square between groups , MSA = SSA/k-1 =    96.0000
  
mean square within groups , MSE = SSE/N-k =    60.0000

F-stat = MSA/MSE =    1.6000

anova table
	SS	df	MS	F	p-value	F-critical
Between:	192.000	2	96.000	1.600	0.2367	3.739
Within:	840.000	14	60.000
Total:	1032.000	16
					α =	0.05

e) critical value = 3.739

Decision: reject Ho

f)

three assumptions for ANOVA analysis, namely, independence, equal variance, and normality.