The air in poultry-processing plants often contains fungus spores. Inadequate ve

Question

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.

The spore count is clearly higher in the kill room. Give sample means and a 99% confidence interval to estimate how much higher the spore count is in the kill room.

To do this problem correctly you need to think carefully about whether this is really a matched pairs design (one sample with two measurement) or a two sample design.

x¯ (kill): ___2138.5___
x¯ (processing): ___314___

99% confidence interval: ___?___ to ___?___

Explanation / Answer

A) The two different samples have been paired on four days. These are pairs matched into meaningful groups, so they are matched paired data.

B)
We use a paired t-test in this case.
--------------difference
3175 529 = 2646
2526 141 = 2385
1763 362 = 1401
1090 224 = 866

Mean of differences (Kill room - Processing) = 1824.5

Number of cases 4
To find the mean, add all of the observations and divide by 4
Mean 1824.5
Squared deviations
(2646-(1824.5))^2 = (821.5)^2 = 674862.25
(2385-(1824.5))^2 = (560.5)^2 = 314160.25
(1401-(1824.5))^2 = (-423.5)^2 = 179352.25
(866-(1824.5))^2 = (-958.5)^2 = 918722.25
Add the squared deviations and divide by 3

Variance (using n-1) = 2087097/3
Variance 695699
Standard deviation (using n-1) = sqrt(variance) = 834.0857

We use the matched-pairs t-test
The t-critical value with 3 degrees of freedom for a 99% confidence interval (for mean difference) is 5.841.

Sample mean = 1824.5
Standard deviation = 834.0857
Standard error of mean = s / n
Standard error of mean = 834.0857 / 4
SE = 834.0857/2
Standard error of mean 417.0429
Confidence interval 1824.5-(417.0429)(2.353)
and 1824.5+(417.0429)(5.841)
99% confidence interval for difference in means (-611.45, 4260.45)

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