BuyFind

Precalculus: Mathematics for Calcu...

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

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.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 8P , additional homework tip  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

Answer to Problem 8P

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.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 8P , additional homework tip  2

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

Answer to Problem 8P

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

Answer to Problem 8P

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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