SOLUTION: The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durba

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Question 1183457: The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 31 orders from Limpopo branch had an average value of R355.20 with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample standard deviation of R162.20. Can the operations managers conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch? Show the null and alternative hypothesis for the test and draw the appropriate conclusion. Compute the P-value
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: L-D <=0
Ha: L-D >0
alpha =0.03 p{reject Ho|Ho true}
test is a t 0.985, df=64 (n1+n2-2)
critical value t >1.91
calculation is t=(355.20-265.60)/sqrt(151.50^2/31+(162.20^2/35))
=89.6/sqrt (1492.08)
=2.32
reject Ho and conclude that Limpopo is doing better than Durban.
p-value = 0.024 (calculator)