A)Find a 95% confidence interval for the mean noise level for streets whose average speed is 30 kilometers per hour. The 95% confidence interval for the mean is? How much noisier are streets where cars travel faster? An article reports noise levels in decibels and average speed inkilometers per hour for a sample of roads. The following table presents the results.NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.SpeedNoise28.2678.136.2279.638.7381.029.0778.730.2878.630.2578.429.0378.433.1779.6

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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

The 95% confidence interval for the mean is?

How much noisier are streets where cars travel faster? An article reports noise levels in decibels and average speed in
kilometers per hour for a sample of roads. The following table presents the results.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
Speed
Noise
28.26
78.1
36.22
79.6
38.73
81.0
29.07
78.7
30.28
78.6
30.25
78.4
29.03
78.4
33.17
79.6

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

For the variable noise level in streets, using Excel to calculate the values of sample mean and standard deviation as:

The function

gives Mean $\bar{x}$ = 79.05 and the function

gives standard deviation s = 0.96214

The 95% confidence interval for mean noise level is given as:

$(\bar{x} \pm z_{α / 2} \times \frac{s}{\sqrt{n}})$

where $z_{α / 2} = 1.96$

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