How much noisier are streets where cars travel faster? The article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatpipat, Journal of Transportation Engineering, 1999:152-159) reports noise levels in decibels and average speed in kilometers per hour for a sample of roads. The following table presents the results.

a. Compute the least-squares line for predicting noise level \((y)\) from speed \((x)\).

b. Compute the error standard deviation estimate \(s\).

c. Construct a \(95 \%\) confidence interval for the slope.

d. Find a \(95 \%\) confidence interval for the mean noise level for streets whose average speed is 30 kilometers per hour.

e. Can you conclude that the mean noise level for streets whose average speed is 30 kilometers per hour is greater than 78 decibels? Perform a hypothesis test and report the \(P\)-value.

f. Find a \(95 \%\) prediction interval for the mean noise level for streets whose average speed is 30 kilometers per hour.

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Speed 28.26 36.22 38.73 29.07 30.28 30.25 29.03 33.17 Noise 78.1 79.6 81.0 78.7 78.6 78.5 78.4 79.6