A packing company investigates a national training consultant in hopes of improving productivity on the packing line. The national consultant agrees to work with 18 employees, collecting productivity data for each employee before the training program and after the training program. The training program will be implemented if the average product packed increases by more than 10 cases per day per employee.

The 95% confidence interval for the mean change in package production μd = μAfter - μBefore is (9.5, 11.4).

Interpret the confidence interval.
A) We are 95% confident that each employee produces between 9.5 and 11.4 more packages after the training.
B) We are 95% confident that the mean number of packages produced per employee decreased by 9.5 to 11.4 packages after the training.
C) We are 95% confident that the mean number of packages produced per employee increased by 9.5 to 11.4 packages after the training.
D) We are 95% confident that the training program had a significant impact on production.

C?

What about A ?

Yes, the correct interpretation of the confidence interval is C) "We are 95% confident that the mean number of packages produced per employee increased by 9.5 to 11.4 packages after the training."

In a confidence interval, the lower and upper bounds estimate the range within which the true population parameter is likely to lie, with the specified level of confidence (in this case, 95%). In this case, the confidence interval (9.5, 11.4) suggests that the average increase in package production per employee after the training is somewhere between 9.5 and 11.4.

Since the lower bound of the confidence interval is positive (9.5), it implies that the training program had a positive impact - it increased the mean number of packages produced per employee. Therefore, we can conclude that the training program was likely effective in improving productivity on the packing line.