Question

An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the following data after traveling each route for one week. Route 1 Route 2 Route 3 35 29 35 25 32 25 28 24 29 24 26 27 21 22 22 Click here for the Excel Data File Click here for the CSV Data File 6.1. Construct an ANOVA table. (Round "Sum Sq' to 1 decimal place, "Mean Sq" and "Fvalue" to 2, and round the p-value to 4 decimal places, Enter options(digits 10) into your R console before running the ANOVA.) Answer is complete and correct. ANOVA Source of Variation DF Sum Sg Mean Sq Route F value 7.30 150.9 1240 Residuals Prpf) 0.0084 75.47 10.33 3-2. At the 5% significance level do the average commute times differ slanificantly between the three routes. Assume that commute < Prey 8 of B !!! Next

Answer 1

anova table
	SS	df	MS	F	p-value	F-critical
Between:	150.9	2	75.47	7.30	0.0084	3.89
Within:	124.0	12	10.33
Total:	274.9	14
					α =	0.05
			conclusion :	p-value<α , reject null hypothesis

2)

yes, times differes, as p value is less than 0.05

b)

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	12
MSE	10.333
q-statistic value(α,k,N-k)	3.7700

critical value = q*√(MSE/n)

confidence interval = mean difference ± critical value

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ2-µ1	-5.20	5.42	-10.62	0.22	means are not different
µ3-µ1	-7.60	5.42	-13.02	-2.18	means are different
µ3-µ2	-2.40	5.42	-7.82	3.02	means are not different

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

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