Question

Exposure to endotoxins may have an impact on how sensitive someone is to allergies. To study endotoxins, researchers measured concentrations of dust (EU/mg) in urban (U) and farm (F) homes and record the following measurements: U: 6.0 5.0 11.0 33.0 4.0 5.0 120.0 18.0 35.0 13.0 23.0 F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 a) Calculate the sample mean for U and F. What is the difference between the means x¯U - x¯F ? Please report your answer to 3 decimal places. (For example 3.1119 - 2.0091 = 1.1028 is rounded to 1.103.)

Answer 1

a)

Sample mean for U: 24.818

Sample mean for F: 9.15

Explanation:

a)

Sample mean for concentration of dust in urban homes (11 samples)

`\bar U=(6+5+11+33+4+5+120+18+35+13+23)/(11)=(273)/(11)=24.8181`

Sample mean for concentration of dust in farm homes (14 samples)

`\bar F=(4+14+11+9+9+8+4+20+5+8.9+21+9.2+3+2)/(14)=(128.1)/(14)=9.15`

b)

The difference between the means of concentration of dust in urban homes and farm homes is

`\bar U-\bar F=24.8181-9.15\approx 15.668`