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The air quality (PM10) has been measured at an airport at 20 representative days
and showed a mean value of 41µg=m3 and a standard deviation of 3:7µg=m3. In the
city center, over 15 representative days a mean of 44µg=m3 and a standard deviation
of 3:5µg=m3 has been observed.
(a) Is there a statistically significant difference in the air quality between the two
locations (α = 0:05; use for the t-quantile df = 20 + 15 - 2 = 33)?
(b) The European acceptance limit is 50µg=m3. If the samples are representative
for a complete year and the air quality values are normally distributed: What
is the expected proportion of days with inacceptable air quality?
Note that in reality the air quality measures follow rather a logarithmic than a
normal distribution.