Question

A researcher wishes to see whether there is any difference in the average starting salary for a
college graduate's first job after graduating with the degrees shown. She randomly sampled graduates in
each degree and the results are listed. At cr = .10, can we conclude that there is a difference in the average
starting salaries of these graduates?

Economics	42	53	49	44	54
Medicine	69	54	58	64	56
History	35	40	53	42
X1=	X2=	X3=	XGM=

Economics Medicine History Xl=
42 69 35 Xo =
53 54 40 Xz=
49 5B 53 v- Lfrt
-

44 64 42
54 56

LXt-242; IXz-301; ZXz-L7}; s12: I sz2: : s3z:
a) What are the null and alternative hypotheses?
b) What is the critical value for F at u= .10?

c) What is the test value for F?

d) What is the decision?

e) Summary statement:

Answer 1

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

b)

F-critical =2.860

...............

c)

treatment	G1	G2	G3
count, ni =	5	5	4
mean , x̅ i =	48.400	60.20	42.50
std. dev., si =	5.3	6.2	7.6
sample variances, si^2 =	28.300	38.200	57.667
total sum	242	301	170				713	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	50.93
( x̅ - x̅̅ )²	6.394	85.959	71.041
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	31.968	429.797	284.163				745.9285714
SS(within ) = SSW = Σ(n-1)s² =	113.200	152.800	173.000				439.0000

no. of treatment , k =   3  
df between = k-1 =    2  
N = Σn =   14  
df within = N-k =   11  
      
mean square between groups , MSB = SSB/k-1 =    745.9286/2=   372.9643
mean square within groups , MSW = SSW/N-k =    439/11=   39.9091
      
F-stat = MSB/MSW =    372.9643/39.9091=   9.35

anova table
	SS	df	MS	F		F-critical
Between:	745.9	2	373.0	9.35		2.860
Within:	439.0	11	39.9
Total:	1184.9	13

................

d)

F stat > critical value , reject Ho

............

e)

there is difference in the average starting salary for a college graduate's first job after graduating with the degrees shown

..................

Please let me know in case of any doubt.

Thanks in advance!

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