Question

Please, I need help with this question not with software. The old fashion way is very helpful/

6. Ryan wants to know if weather affects mood.  To that end, he asks the same 15 people to rate their moods at three different times – when it is raining, when it is sunny and when it is snowing.  The data follows.  Does weather significantly affect mood? SS_subjects = 100

Raining	Sunny	Snowing
M=5, s=1.5, n=15	M=8, s=1.1, n=15	M=8.4, s=3.1, n=15

Answer 1

Ho: weather does not significantly affect mood

H1: weather does significantly affect mood

	raining	sunny	Snowing
count, ni =	15	15	15
mean , x̅ i =	5.000	8.00	8.40
std. dev., si =	1.500	1.100	3.100
sample variances, si^2 =	2.250	1.210	9.610
total sum	75	120	126		321	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				7.13
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	4.551	0.751	1.604
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	68.267	11.267	24.067		103.6
SS(within ) = SSW = Σ(n-1)s² =	31.500	16.940	134.540		182.980

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   45
df within = N-k =   42
  
mean square between groups , MSB = SSB/k-1 =    51.8000
  
mean square within groups , MSW = SSW/N-k =    4.3567
  
F-stat = MSB/MSW =    11.8898
P value =   0.0001

anova table
	SS	df	MS	F	p-value
Between:	103.600	2	51.800	11.890	0.0001
Within:	182.980	42	4.357
Total:	286.580	44

p value <α=0.05, reject Ho

there is enough evidence that weather does significantly affect mood at α=0.05