Question

A problem with a telephone line that prevents that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data PHONE represents samples of 20 problems reported to two different offices of a telephone company of a telephone company and the time to clear these problems (in minutes) from the customers’ lines:
Central office 1, time to clear problems in minutes
1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10
1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97
Central office 2, time to clear problems in minutes
7.53 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02
3.75 0.65 1.95 0.60 1.53 4.23 0.08 1.48 1.65 0.72
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 α=0.05).
b. Assuming that the population variances from both offices are NOT equal, is there evidence of a difference in the mean waiting time between the two offices? (Use α=0.05).
c. Find the p-value in (a) and interpret its meaning
d. What other assumptions is necessary in (a)
e. 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.

Answer 1

A problem with a telephone line that prevents that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data PHONE represents samples of 20 problems reported to two different offices of a telephone company of a telephone company and the time to clear these problems (in minutes) from the customers’ lines: Central office 1, time to clear problems in minutes 1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10 1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97 Central office 2, time to clear problems in minutes 7.53 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02 3.75 0.65 1.95 0.60 1.53 4.23 0.08 1.48 1.65 0.72 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 alpha=0.05). I ran a 2-sample t-test with pooled variances to get: t = 0.3538 p = 0.7254 Conclusion: Fail to reject equality of the means. ---------------------------------------------------------- b. Assuming that the population variances from both offices are NOT equal, is there evidence of a difference in the mean waiting time between the two offices? (Use alpha=0.05). I ran a 2-sample t-test without pooling the variances to get: p = 0.7254 Conclusion: Fail to reject equality of the means. ------------------------------------------------------ c. Find the p-value in (a) and interpret its meaning More than 72% of test results would provide stronger evidence for rejecting the equality of the means. ----------------------------------------- d. What other assumptions is necessary in (a) e. 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. I ran a 2-Sample T-Interval program on a TI calculator to get: 95% CI: 9-0.9537 , 1.3577) ================================ Cheers, Stan H.