A problem with a telephone line that prevents a customer from receiving or makin

Question

A problem with a telephone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telephone company. Samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines are provided. The following is a sample of 20 problems reported to the first office and the time (in minutes) to clear those problems. 1.66
1.82
0.61
2.64
0.36
1.51
4.17
3.83
1.73
3.02
1.16
0.31
0.81
1.81
0.82
1.03
6.44
3.96
5.72
0.92

The following is a sample of 20 problems reported to the second office and the time (in minutes) to clear those problems.

7.36
3.76
0.05
1.08
0.29
0.42
3.3
2.07
0.67
4.18
3.55
0.59
1.86
0.28
1.67
4.46
0.18
1.33
1.43
0.89

QUESTION: 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. The confidence interval is:

Explanation / Answer

For 95% cofnidence intevral degree of freedom=n1+n2-2=20+20-2=38

Critical t=2.024

From followig calculations using excel we get

95% cofnidence intevral =(xbar1-xbar2)± t*Pooled Standard devaition

=(2.22-1.97)±2.024*1.84

=(-3.47 , 3.97)

Pooled Variance varp

=((n1-1)*var1+(n2-1)var2))/(n1+n2-2)

(19*3.13+19*3.63)/38

=3.38

First office Second office Mean xbar 2.22 1.97 Standard deviation s 1.77 1.90 Sample Size n 20 20 Variance 3.13 3.63

Pooled Variance varp

=((n1-1)*var1+(n2-1)var2))/(n1+n2-2)

(19*3.13+19*3.63)/38

=3.38

Pooled Standard deviation sp=sqrt(varp) sqrt(3.38)=1.84

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