Question 1181998: A hospital is studying the delivery time of two laundry companies. The hospital has been using Company A for the past year and is basically satisfied with time the company takes to return laundry to the hospital. The hospital is prepared to stay with Company A if the mean delivery time is the same as or less than that of a competitor company - Company B. However, if the hospital finds that the mean delivery time of Company B is less than that of Company A, it will start using the laundry services of Company B. Independent samples showed the following delivery time characteristics for the two companies.
Company A
n1 = 20
X1 = 10 days
s1 = 3 days
Company B
n1 = 30
X2 = 12.5 days
s1 = 2 days
What are the null and alternative hypotheses for this situation?
With an α = .05, what is your conclusion for the hypotheses from part (a)? What action do you recommend in terms of which laundry company the hospital should contract?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: meanA <=mean B
Ha: mean A > mean B
alpha=0.05 P{reject Ho| Ho true}
test is a 2-sample t-test
reject Ho if t>1.675
test is a t (df=48)=(meanA-mean B)/sqrt (s1^2*/na)+(s2^2/(nb))
=(-2.5)/sqrt((9/20)+(4/30))
=-2.5/sqrt(0.583)
=-3.27
fail to reject Ho; indeed, the data themselves show that A has a a statistically smaller mean than B.
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