0:00

Mathematical Statistics with Applications

The EPA has set a maximum noise level for heavy trucks at 83 decibels (dB). The manner in which this limit is applied will greatly affect the trucking industry and the public. One way to apply the limit is to require all trucks to conform to the noise limit. A second but less satisfactory method is to require the truck fleet's mean noise level to be less than the limit. If the latter rule is adopted, variation in the noise level from truck to truck becomes important because a large value of $\sigma^{2}$ would imply that many trucks exceed the limit, even if the mean fleet level were 83 dB. A random sample of six heavy trucks produced the following noise levels (in decibels):

$\begin{array}{llllll}85.4 & 86.8 & 86.1 & 85.3 & 84.8 & 86.0 .\end{array}$

Use these data to construct a $90 \%$ confidence interval for $\sigma^{2}$, the variance of the truck noiseemission readings. Interpret your results.