Answer to Question #237143 in Statistics and Probability for esha

Question

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 the 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 manager conclude, at the 3% significance level,
that the Limpopo branch is performing better than the Durban branch?
Show the null and alternative hypotheses for the test and draw the appropriate conclusion.
Compute the p-value.

Answer 1

QUESTION

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 the 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 manager conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch?

Show the null and alternative hypotheses for the test and draw the appropriate conclusion.

Compute the p-value.

SOLUTION

H_o: $L-D\le0$

H_a: $L-D\gt0$

alpha = 0.03 p{reject H_o| H_o true}

test is a t 0.985, $df=64 (n1+n2-2)$

critical value $t\gt1.91$

calculation is $t=\frac{\big(355.20-265.60\big)}{\sqrt{\frac{151.50^2}{31}+\frac{162.20^2}{35}}}$

$=\frac{89.6}{\sqrt{1492.08}}$

=2.32

ANSWER: Reject H_o (null hypothesis) and conclude that Limpopo is doing better than Durban.

p-value = 0.024 (calculator)