Exposure to microbial products, especially endotoxin, may have an impact on vuln

Question

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The following are data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes. U: 6.0 5.0 11.0 33.0 4.0 5.0 60.0 18.0 35.0 27.0 23.0 F: 4.0 14.0 12.0 8.0 8.0 6.0 2.0 19.0 5.0 9.6 24.0 9.9 3.0 0.3 Determine the sample mean for each sample. (Round your answers to two decimal places.) How do they compare? The average endotoxin concentration in urban homes is more than double the average concentration in farm homes. The average endotoxin concentration in farm homes is more than double the average concentration in urban homes. The average endotoxin concentration is about the same m both urban and farm homes. Determine the sample median for each sample. How do they compare? The median endotoxin concentration in farm homes is roughly double the median concentration in urban homes. The median endotoxin concentration in urban homes is roughly double the median concentration in farm homes. The median endotoxin concentration is about the same in both urban and farm homes. Why is the median for the urban sample so different from the mean for that sample? The mean and median for urban homes are so different because the measure different aspects of the distribution. The mean and median for urban homes are so different because there are fewer observations. The mean and median for urban homes are so different because the few large values raise the mean but not the median. Calculate the trimmed mean for each sample by deleting the smallest and largest observation. (Round your answers to two decimal places.) What are the corresponding trimming percentages? (Round your

Explanation / Answer

(a) Sample means:

Urban Homes: 21.55 EU/mg.

Farm Homes: 8.52 EU/mg.

Hence, the average endotoxin concentration in Urban homes is more than double the average of concentration in farm homes. (Ans).

(b) Sample Medians:

Urban Homes: 17 EU/mg.

Farm Homes: 8 EU/mg.

  Hence, the median endotoxin concentration in Urban homes is roughly double the median concentration in farm homes. (Ans).

(c) The median for the urban sample is so different from the mean of that sample because few large values raise the mean but not the median. (Ans).

(d) By deleting the smallest and largest observations the trimmed means are:

Urban Homes: 17 EU/mg. (Ans).

Farm Homes: 7.96 EU/mg. (Ans).

For Urban Homes, after trimming the average is reduced by {(21.55 - 17) / 21.55} * 100% = 21.11%. (Ans).

For Farm Homes, after trimming the average is reduced by {(8.52 - 7.96) / 8.52} * 100% = 6.57%. (Ans).

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