Question

Flight 1	-2	-1	-2	2	-2	0	-2	-3
Flight 19	19	-4	-5	-1	-4	73	0	1
Flight 21	18	60	142	-1	-11	-1	47	13

Listed below are departure delay times (minutes) for american Airline flights from New York to Los Angeles. Negative values correspond to flights that departed early.

Use a 0.05 significance level to test the claim that the different flights have the same mean departure delay time.What is the critical value (F-value)? [Round to 4 decimal places]

Answer 1

treatment	Flight 1	Flight 19	Flight 21
count, ni =	8	8	8
mean , x̅ i =	-1.250	9.88	33.38
std. dev., si =	1.6	26.6	50.3
sample variances, si^2 =	2.500	709.839	2525.411
total sum	-10	79	267				336	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	14.00
( x̅ - x̅̅ )²	232.563	17.016	375.391
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	1860.500	136.125	3003.125				4999.75
SS(within ) = SSW = Σ(n-1)s² =	17.500	4968.875	17677.875				22664.2500

no. of treatment , k =   3  
df between = k-1 =    2  
N = Σn =   24  
df within = N-k =   21  
      
mean square between groups , MSB = SSB/k-1 =    4999.75/2=   2499.8750
mean square within groups , MSW = SSW/N-k =    22664.25/21=   1079.2500
      
F-stat = MSB/MSW =    2499.875/1079.25=   2.32

ANOVA
	SS	df	MS	F	p-value	F-critical
Between:	4999.75	2	2499.88	2.316	0.1233	3.467
Within:	22664.25	21	1079.25
Total:	27664.00	23
					α =	0.05

critical F value= 3.4668

there is insufficient evidence to reject the  claim that the different flights have the same mean departure delay time.