How much noisier are streets where cars travel faster? The article "Modeling of Urban AreaStop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatpipat, Journal ofTransportation Engineering, 1999:152–159) reports noise levels in decibels and averagespeed in kilometers per hour for a sample of roads. The following table presents the results.SpeedNoise28.2678.136.2279.638.7381.029.0778.730.2878.630.2578.529.0378.433.1779.6Compute the least-squares line for predicting noise level (y) from speed (x).b. Compute the erTor standard deviation estimate s.Construct a 95% confidence interval for the slope.Find a 95% confidence interval for the mean noise level for streets whose averagespeed is 30 kilometers per hour.Can you conclude that the mean noise level for streets whose average speed is 30kilometers per hour is greater than 78 decibels? Perform a hypothesis test and reporta.C.d.e.the P-value.f.Find a 95% prediction interval for the mean noise level for streets whose average speedis 30 kilometers per hour.

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures, in degrees Celsius, and mean coral growth, in centimeters per year, over a several‑year period at locations in the Gulf of Mexico and the Caribbean Sea. The table shows the data for the Gulf of Mexico. Sea surface temperature 26.726.7 26.626.6 26.626.6 26.526.5 26.326.3 26.126.1 Growth 0.850.85 0.850.85 0.790.79 0.860.86 0.890.89 0.920.92 (b) Find the correlation ?r step by step. Round off to two decimals places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for ?r . Round your answer to three decimal places.
The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
In experiments to determine the effectiveness of drugs such as anti-fungal ointments that are applied to the skin, the concentration of the drug in a patient’s skin must be measured. The article “Determining Bioequivalence of Topical Dermatological Drug Products by Tape- Stripping” (W. Navidi, A. Hutchinson, et al., Journal of Pharmacokinetics and Pharmacodynamics, 2008:213–220) describes an improved method of measuring that is designed to ensure that all the drug in the skin is recovered. Assume that in an experiment using the old method, the mean amount of drug recovered from a sample of 49 patients was 105 ng with a standard deviation of 20 ng, and that in an experiment using the new method the mean amount of drug recovered in a sample of 35 patients was 117 ng with a standard deviation of 15 ng. Find a 98% confidence interval for the difference in the mean amounts recovered between the two methods.

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