Research in the International Journal of Foresting Engineering (Vol. 19, 2008) investigated the muscle activity patterns in the neck and upper extremities among forestry vehicle operators. Two types of harvesting vehicles — Timber jack and Valmet — were compared since they differed dramatically in design of the control levers. Independent random samples of 7 Timber jack and 6 Valmet harvester operators participated in the study. Muscle rest (seconds per minute) in the right trapezius (a neck muscle) was determined for each operator. The 7 Timber jack operators had a mean muscle rest of 10.35 seconds/minute, while the 6 Valmet operators had a mean of 3.30 seconds/minute.

a. Explain why one cannot make any reliable inferences about (μ_T - μ_V), the true mean difference in muscle rest in the right trapezius of Timber jack and Valmet harvest or operators based on the information provided. 

b. Suppose the standard deviations for the samples of Timber jack and Valmet operators are 4.0 and 2.5 seconds/ minute, respectively. Use this additional information to construct a 99% confidence interval for (μ_T - μ_V). Practically interpret the resulting interval.

c. What assumptions about the data must be made in order for the inference, part b, to be valid?