Chapter 11.5, Problem 20E

To determine

To calculate:

Value of interval and correct the error.

Answer to Problem 20E

Interval percentages are $59\%$ and $63\%$ and error observed in the result of the given equation.

Explanation of Solution

Given information:

Margin of error: $0.02$

Percentages: $61\%$

Calculation:

In order to find the interval of the survey,

  $I=P-M_e$

Where,

  $I=$ Interval of the survey.

  $P=$ Percentage.

  $M_e=$ Margin of error.

Here given equation is,

Margin of error is,

  $=\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{2500}}=0.02$

But by using given margin of error $2\%$ calculations for interval is,

  $\begin{array}{l}=\pm 61\%-2\%\\ =59\%and63\%\end{array}$

Hence, percentages are $59\%$ and $63\%$

Error observed in the result of the given equation.