Question

20.40 Fungus in the air. 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 (CFU)" 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.27 FUNGUS Kill room Day 1 3175 529 2646 Day 2 2526 141 2385 Day 3 1763 362 1401 Day 4 1090 2 24 866 Processing Kill room-processing (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?

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Answer 1

1 2 day 1 Kill room | Processing 3175 3 29 2526 141 1763 362 1090 224 Total (d-dbar)^2 2646 | 674862.25 2385 314160.25 1401 179352.25 866 918722.25 7298 2087097 dbar BESV 1824.5 695699 t critical 2.3533634

Processing 1 daykill room! 3175 2 2526 1263 3 fd-dbar2 =102-$C$8) 03-$8)^2 =fD4-$C$8)2 ={D5-$C$8142 SUMID2:05) SUME2:55) tcritical =TINV.2T10.1.3)

The data is on matched pairs. Because there will be a variation in weather Conditions between days 1, 2,3,4. These variations may be humidity, temperature cte. which effect the growth of fungus, so, similar weather conditions are these on different days. witch affect the clata. Hence we go for matched paired test. " 6) The 20. Confidence interval for difference of means is d I tai sela). Here da means of diffuse ne E means of difference in GFO count

in killing and processing room on different dorms, days. se is stand and the son of a which is given by sim sa II (di-d)" _ I Z(di - d.) 2 di = wi-yi à Edisdi. i is cpo count in Killing som ai is cfo count in processing doom excel All calculations are done is d = 18,24.5 seca)=1695699. 1173,924.15 = 417.0459 | Critical value of t dobitation at B degrees of freedom and of level of significance is 2.3534. Upper limit of confidence internal a t tai seld) 18245 t 2:2834 (417.0429)

= 2805.9688 Lower limit is ā- the (S.E: (a)) = 18245-23534 (417.0429) - 1924.5 - 981.4688 = $43.0312 Hence 90 to confidence sitaval too difesenice of means (CFO count in Killing & processing doom) is (843-0312, 280519688), Mean CFO count of billing som = 21 38.5 i n processing room 316 Difference in these mans. 2138.5-314 21824:57 Sonce under hall hypothesis difference in CFO casts between Rooms is zero and o is not contained in confidence

interval we can conclude that CFO count is significantly different in two dooms. in fact it is higher in billing toom comp and to processing rooms, looking at confidence interval as it contains positive limits. It B a sough approximation to use t test because assumption of t test are not verified before applying t test and it says that data: should be normally distributed