Question

A certain statistics instructor participates in triathlons. The accompanying table lists times​ (in seconds) he recorded while riding a bicycle. He recorded every time he rode and randomly picked five laps through each mile of a​ 3-mile loop. Use a .05 significance level to test the claim that it takes the same time to ride each of the miles. Mile 1 194 205 203 202 201

Mile 2 198 201 200 196 200

Mile 3 215 211 209 212 209

a) State the null and alternative hypothesis (2 points).

b) Check the requirements (3 points)

c) Carry out the hypothesis test (make sure you write everything down) (3 points)

. d) What is your conclusion? (2 points)

e) Does one of the miles appear to have a​ hill? (2 points)

Answer 1

a)

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

........

	A	B	C
count, ni =	5	5	5
mean , x̅ i =	201.000	199.00	211.20
std. dev., si =	4.183	2.000	2.490
sample variances, si^2 =	17.500	4.000	6.200
total sum	1005	995	1056		3056	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	203.73
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	7.471	22.404	55.751
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	37.356	112.022	278.756		428.1333
SS(within ) = SSW = Σ(n-1)s² =	70.000	16.000	24.800		110.8000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    214.0667
  
mean square within groups , MSW = SSW/N-k =    9.2333
  
F-stat = MSB/MSW =    23.1841

anova table
	SS	df	MS	F	p-value	F-critical
Between:	428.13	2	214.07	23.18	0.0001	3.89
Within:	110.80	12	9.23
Total:	538.93	14

     

..........

α =    0.05
conclusion :    p-value<α , reject null hypothesis    

so, means are different

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

THANKS

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