A problem with a phone line that prevents a customer from receiving or making ca
ID: 3207694 • Letter: A
Question
A problem with a phone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telecommunications company. The file PHONE contains samples of 20 problems reported to two different offices of telecommunications company and the time to clear these problems (in minutes)from the customers lines
a. assuming that the population variances from both offices are equal, is there evidence of a difference in the mean waiting time between the two offices? (Use a= 0.05), and find the FSTAT (round to three decimal places)
b. find the p-value in (a) and interpret its meaning.
c. What other assumption is necessary in (a)?
d. Assuming that the population variances from both offices are equal, construct and interpret a 95% confidence interval estimate of the difference between the population means in the two offices?
Telephone problem clear times Time Location | Time Location 1.19 7.65 1 .94 3.12 0.88 0.09 3.09 044 0.63 0.61 4.33 373 4.71 208 1.59 0.59 3.65 3.61 0.97 442 0.62 0.58 1.04 1.47 0.54 0.93 1.63 1.18 471 7.18 0.08 4.34 1.21 5.93 196 0.97 0.85 Time Location | Time Location a-2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2-a- 52963138912864318165 m-6 1 0 2 6 6 7 0 5 6 4 5 6 5 670298-m T7 3 0 1 0 0 3 2 0 3 4 0 1 0 140-10T a-1 1-a he 9 4 8 9 4 4 3 1 9 5 7 2 4 7 388437e- m-1 9 8 0 4 3 3 7 5 6 9 6 0 4 911399-m TI 1 1 0 3 0 1 4 4 1 3 0 0 1 1 0 17450TExplanation / Answer
a)
H0: 1 = 2
H1: 1 2
S2P=(n1-1)S12+(n2-1)S22/(n1-1)(n2-1)
=(19)(1.97)^2+(19)(1.95)^2/(19)(19)
=73.7371+72.2475/361
=0.4044
t=(X1-X2)-(µ1- µ2)/sqrt(S2P)(1/n1+1/n2)
(2.3895-2.0505)-0/sqrt(0.4044)(1/20+1/20)
0.339/0.2011
1.6857
At a=0.05, critical value is 2.0244 and t-test is 1.6857 and hence it is not in the rejection region and hence you cannot reject H0.
F-STAT=S12/ S22=(1.97)^2/(1.95)^2=3.8809/3.8025=1.02
b)
The P-Value is .100049.
c)
Samples are randomly and independently drawn
d)
(X1-X2)+-ta/2*sqrt(1/n1+1/n2)
0.339+-2.0244*0.2011
0.339+-0.4071
LL=-0.0681
UL=0.7461
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