The manager of a soda bottling plant is interested in comparing the performance of two bottling machines, the old machine and a new machine that has just been purchased. For each machine she selects 10 one-hour periods at random and records the number of crates of bottles completed in each hour. The table below gives the results.
| New |
82 |
82 |
81 |
79 |
82 |
81 |
79 |
82 |
82 |
82 |
| Old |
77 |
79 |
79 |
75 |
78 |
75 |
78 |
78 |
84 |
77 |
(a) Does this data provide evidence that the new machine is faster than the old machine? (Give details.)
(b) Find a 90% confidence interval for the difference between the two means.