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. a) Explain carefully why these are matched pairs data. b) The spore count is clearly higher in the kill room. Give the sample mean and conduct a hypothesis test to estimate if the difference is statistically significant. Your answer should include your hypotheses, test statistic, p-value, and conclusion. Use alpha = 0.01. c) You will often see t procedures used for data like these. You should regard the results as only rough approximations. Why?

Explanation / Answer

Part A)

A matched pairs design is a special case of a randomized statistical design. It can be used when the experiment has only two treatment conditions; and subjects can be grouped into pairs. Then, within each pair, subjects are randomly assigned to different treatments. Here in the above questions groups are Kill Room and Processing, and pairs are Day1, Day2, Day3 and Day4.

Part B)

Hypothesis would be;

Null hypothesis : There is no significant difference in the means of spore count of Kill Room and Processing

VS

Alternative Hypothesis : There is a significant difference in the means of spore count of Kill Room and Processing

Test Statistics:

From the above table we see P(T<=t) two tail is 0.022099 which is greater than 0.01, hence we reject our null hypothesis and conclude that there is a significant difference in the mean of spore count of Kill Room and Processing.

part C)

Assumptions Underlying the t Test

The above assumption may not be valid with some of the real life data, hence t test could be a rough test, instead we need to see the cause of real difference in mean spore count.

t-Test: Paired Two Sample for Means Kill Room Processing Mean 2138.5 314 Variance 821613.6667 28852.66667 Observations 4 4 Pearson Correlation 0.502600015 Hypothesized Mean Difference 0 df 3 t Stat 4.374850069 P(T<=t) one-tail 0.011049668 t Critical one-tail 4.540702859 P(T<=t) two-tail 0.022099336 t Critical two-tail 5.84090931

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