Final answer:
Control charts are the appropriate statistical tool for monitoring and controlling the process when multiple sample means are to be evaluated for consistency and determining if a process is in statistical control.
Step-by-step explanation:
The statistical tool likely to be employed for monitoring and controlling the process when six samples with 10 observations each have been obtained, and the sample means (in minutes) are computed is a control chart. Control charts are used in process monitoring to determine if a process is in a state of statistical control and to identify the presence of special-cause variation, which is variation due to specific, identifiable causes, as opposed to common-cause variation, which is inherent to the process.
Other options like regression analysis, T-test, Chi-square test, and Analysis of Variance (ANOVA) are used for different purposes such as modeling relationships between variables, comparing means between two groups, testing for independence or goodness-of-fit, and comparing means across multiple groups, respectively. However, given the context of process control and the kind of data provided (sample means), control charts are the appropriate statistical tool.