# To graph: The scatter plot of the data. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 8P

(a)

To determine

## To graph: The scatter plot of the data.

Expert Solution

### Explanation of Solution

Graph:

Consider the Noise level in decibel as the x coordinates and the M.R.T score as the y coordinates.

The scatter plots of the given data are shown below in Figure 1. From Figure 1, all the points are plotted on the graph. No two points coincide each other.

(b)

To determine

### To find: The regression line that represents the given data and draw the graph for it.

Expert Solution

The regression that represents the given data is y=3.902x+419.7 .

### Explanation of Solution

By the use of online calculator, the regression line for the given data obtained is y=3.902x+419.7 , where M.R.T score is the y-intercept and noise level is the x-intercept.

The above regression line is in the form of linear equation.

Therefore, the linear function that represents the given data is y=3.902x+419.7 .

The graph that represents the equation y=3.902x+419.7 is shown below in Figure 1. From Figure 2, the graph for the linear equation y=3.902x+419.7 is a straight line.

(c)

To determine

### To find: The correlation coefficient and to check whether the linear model appropriate or not.

Expert Solution

The correlation coefficient is 0.76 .

### Explanation of Solution

Formula used:

The formula for the correlation coefficient is r=n(xy)(x)(y)(nx2(x)2)(ny2(y)2) .

Calculation:

Compute the values of the summation of x, y, xy, x2 , y2 and are shown in below table.

 x y xy x2 y2 −10 99 −990 100 9801 −6 91 −546 36 8281 −2 84 −168 4 7056 2 70 140 4 4900 6 47 282 36 2209 10 23 230 100 529 14 11 154 196 121 ∑x =8 ∑y =425 ∑xy =−898 ∑x2 =476 ∑y2 =32897

It is observed that the value of n = 7.

Substitute the values that are obtained in the table to compute the correlation coefficient by using the above mentioned formula.

r=7(898)(8)(425)(7(476)(8)2)(7(32897)(425)2)=62893400(333264)(230279180625)=9689(3268)(49654)=9689162269272

On further simplification.

r=968912738.49567=0.76

Thus, the value of the correlation coefficient is 0.76 .

(d)

To determine

### To find: The estimate value of the intelligibility of a sentence at a 94-dB.

Expert Solution

The estimate value of the intelligibility of a sentence at a 94-dB is 52.912 %.

### Explanation of Solution

Consider the noise level at 94-dB.

From part (b), it is obtained that the linear equation that represents the given data is y=3.902x+419.7 .

Substitute x = 94 in the above equation to compute the M.R.T score.

y=3.902(94)+419.7=366.788+419.7=52.912

Thus, the estimate value of the intelligibility of a sentence at a 94-dB is 52.912 %.

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