18 on mana2e t o ca centers and are working on tr in2 to rea ce the amount of ti

Question

18

on mana2e t o ca centers and are working on tr in2 to rea ce the amount of time customers are p aced on hold is different than the mean hold time for Call Center 2 ou believe e mean hold timear the two call centers are not the sames von start bv Testing the claim that e mean hold time or all enter You wish to test the claim thar the mean hold time tor Call Center 1 s ditterent than the mean hold time for Call Center 2 at a signiticance level ofa You obtain the following two samples of data from each center. Each data point is the amount of time in scconds), a customer is placed on hold. Call Center 1 Call Center 2 .2 42.7 57.2 53.3 50.6 60.2 62.4 49.7 44.9 63.6 61.3 67.0 68.5 43.8 44.7 36.2 39.3 35.7 36.2 58.9 49.9 55.5 2.0 a. What is the test statistic for this sample? test statistic = Round to 4 decimal places. b. What is the p-value for this sample? p-value- Routnd to 4 decimal places. c. The p-value is... less than (or equal to) O greater than d This test statistir leais to a decison to reject the null uccept the ull fail to reject the null e·As such, the final conclusion is that There is sufficient evidence to wretion of the clai that the mean hold time for Call C is differeut than the mean hold time for Call Center 2 There is not sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 The sample data suppart the clai tha ta hodme for Call Center1 is difterent than the mean hold time for Call Center 2 There is not sufficient sample evidence to support the claim that the mcan hold tiae for Call Center 1 is diffcrent than the mean kold tine for Call Center 2

Explanation / Answer

we want tot test the hypothesis

Ho: mu1=mu2 against h1: mu1#mu2

Under H0 the test statistic is

tcal = (xbar-ybar) /S*sqrt(1/n1+1+n2) ~ t n1+n2-2

where S2 = (1/n1+n2-2)*[ sum(xi-xbar)^2+sum(yi-ybar)^2]

xbar= 56.825 ybar=47.17

S= 8.5149

test statistic

t= (xbar-yabar) /S*sqrt(1/n1+1+n2)

= (56.825-47.17)/8.5149* sqrt(1/12+1/10)

t =2.6481

p -value for t-test when tcal =2.6481 and d.f =20 and test is two tailed is

p-value = 0.0154

since p-value is less than level of significane alpha= 0.02.

p-value< alpha hence we reject the null hypothesis H0.

Conclusion: there is sufficient evidance to warrant rejection of the claim that mean hold time for call center 1 is different than mean hold time for call center 2.

xi (xi-xbar)^2 yi (yi-ybar)^2 42.7 199.515625 43.8 11.3569 57.2 0.140625 44.2 8.8209 53.3 12.425625 56.2 81.5409 50.6 38.750625 39.3 61.9369 60.2 11.390625 35.7 131.5609 62.4 31.080625 36.2 120.3409 49.7 50.765625 58.9 137.5929 44.9 142.205625 49.9 7.4529 63.6 45.900625 55.5 69.3889 61.8 24.750625 52 23.3289 67 103.530625 68.5 136.305625

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.