The file contains samples of 20 problems reported to two different offices of a

Question

The file contains samples of 20 problems reported to two different offices of a telecommunication company and the time to clear these problems in minutes from the customers' lines.

PLEASE SHOW ALL WORK

1. 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 at the 0.05 significance level.

2. Find the p-value in question (1) and interpret the meaning.

3. What other assumptions are needed for question (1)?

Time Location 1.48 1 1.75 1 0.78 1 2.85 1 0.52 1 1.60 1 4.15 1 3.97 1 1.48 1 3.10 1 1.02 1 0.53 1 0.93 1 1.60 1 0.80 1 1.05 1 6.32 1 3.93 1 5.45 1 0.97 1 7.55 2 3.75 2 0.10 2 1.10 2 0.60 2 0.52 2 3.30 2 2.10 2 0.58 2 4.02 2 3.75 2 0.65 2 1.92 2 0.60 2 1.53 2 4.23 2 0.08 2 1.48 2 1.65 2 0.72 2

Explanation / Answer

here

from above

here degree of freedom =n1+n2-2=38

and pooled std deviation Sp=((n1-1)s12+(n2-1)s22)/(n1+n2-2))1/2 =1.807

hence std error =Sp(1/n1+1/n2)1/2 =0.5714

hence test stat t=(X1-X2)/std error =0.3544

for above test stat at 38 degree of freedom p value =0.725

asw p value is significantly high then 0.05 level, we can not reject that both mean are equal.

S. no sample 1 sample 2 1.48 7.55 1.75 3.75 0.78 0.1 2.85 1.1 0.52 0.6 1.6 0.52 4.15 3.3 3.97 2.1 1.48 0.58 3.1 4.02 1.02 3.75 0.53 0.65 0.93 1.92 1.6 0.6 0.8 1.53 1.05 4.23 6.32 0.08 3.93 1.48 5.45 1.65 0.97 0.72 total 44.280 40.230 mean 2.214 2.012 std deviation(S) 1.718 1.892

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