The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and "colony-forming units (CFUs)" are counted after an incubation period. Here are data from two locations in a plant that processes 37,000 turkeys per day, taken on four days in the summer. The units are CFUs per cubic meter of air. Day 1 Day 2 Day 3 Day 4
Kill Room 3175 2526 1763 1090
Processing 529 141 362 224
Kill Room - Processing 2646 2385 1401 866

a. Explain carefully why these are matched pairs data.
b. The spore count is clearly higher in the kill room. Give sample means and a 90% confidence interval to estimate how much higher. Be sure to state your conclusion in plain language.
c. You will often see the t procedures used for data like these. You should regard the results as only rough approximations. Why?