Final answer:
The estimated expected (mean) time for project completion is determined using statistical analysis of sample data, including average times and standard deviations. This estimation can inform planning and forecasting efforts in various contexts. Adequate sample sizes, variability, and distribution must be considered to produce reliable estimates.
Step-by-step explanation:
The estimated expected (mean) time for project completion is a metric that uses various samples and data points to estimate an average time frame for completing a given task or project. One specific example mentions the average servicing time for air conditioner units by technicians is approximately one hour with a standard deviation of one hour. For the planning of future tasks, it's suggested to budget an average of 1.1 hours per technician, though whether this is sufficient will depend on various factors such as the actual distribution of servicing times and potential outliers.
Another data point discussed is the mean work week for engineers at a startup. Here, an average of 60 hours is estimated, but survey data from 10 engineering friends yields times that range from 45 to 70 hours. This suggests some variability and that it may not be reliable to assume a significant deviation from the estimated 60 hours without further analysis.
In hypothesis testing, such as determining if the average length of time marathon runners have been running is likely 15 years, one would set up the null hypothesis to state there is no difference from the 15 years, and the alternative hypothesis would claim a significant difference from this value. The provided sample mean and standard deviation would then guide the statistical test to reach a conclusion.
Drawing on the provided examples and expanding the concept, it's clear that the mean expected time for project completion involves a statistical analysis of different measures, such as mean, standard deviation, and sample size to provide an informed estimate. Anomalies and unexpected results can impact these estimations, as can the probabilities associated with exceeding certain thresholds. Ultimately, this estimation aids in planning and forecasting within various business and engineering contexts.