Given your experience as an organizational consultant, you have a client with a telephone company who has requested that you help diagnose a potential problem at the telephone company. Your client explained there has been a problem with a telephone line that is preventing customers from receiving or making calls. The problem is disconcerting to both customers and the telephone company. You want to understand the extent of the problem. Your client has provided you with preliminary data to examine. You have a sample of 20 cases reported by two different offices of the telephone company.
Central Office 1 Time to Clear Problems (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 (minutes)
7.55 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02
3.75 0.65 1.92 0.60 1.53 4.23 0.08 1.48 1.65 0.72
1. Compute the sample size, sample mean, and sample standard deviation for data from Central Office Location 1.
2. Compute the sample size, sample mean, and sample standard deviation for data from Central Office Location 2.
3. Assuming 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) Compute the following:
a. State the null and alternative hypothesis
b. Report the level of confidence
c. Report the degrees of freedom
d. Report the critical values
e. Report the test statistic
f. Find the p-value and interpret its meaning
g. State the decision rule.
h. State the decision.
4. When computing pooled-variance t-tests, what assumptions are necessary?
5. 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.
6. Given your initial analysis of the data, do you believe a problem exists at the client facility that requires further examination? If so, what additional data would you need to analyze to understand the nature of the problem? Be specific in your explanations.