   Chapter 9.5, Problem 47E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Test reliability If a test having reliability r is lengthened by a factor n, the reliability of the new test is given by R = n r 1 + ( n − 1 ) r '  0  <   r   ≤  1 Find the rate at which R changes with respect to n.

To determine

To calculate: The rate at which R changes with respect to n, if a test having reliability r is lengthened by a factor n, the reliability of the new test is given by the expression R=(nr1+(n1)r) at 0r1.

Explanation

Given Information:

A test having reliability r is lengthened by a factor n, the reliability of the new test is given by the expression R=(nr1+(n1)r) at 0r1.

Formula Used:

As per the quotient rule, if two functions are given in the form f(x)g(x), then the derivative is given as:

ddx(fg)=f.gg.fg2.

The rate of the function is the first derivative of the function.

If one function is a sum of multiple functions, then the derivative is:

f(x)=f1(x)+f2(x).

Calculation:

Consider the provided expression, R=(nr1+(n1)r) at 0r1,,

In the expression, the value of,

f(n)=nr

And

g(n)=1+(n1)r=(1+nrr)

Apply the quotient rule of the expression,

ddn(fg)=ddn(nr).(1+nrr)ddn(1+nrr)

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