Chapter 11, Problem 14PT

To determine

To find: The maximum error of estimate for the time spent in the gym using $95\%$ confidence interval.

Answer to Problem 14PT

The correct choice is G.

Explanation of Solution

Given:

The total survey population is $300$ .

The average time spent is $25.3$ minutes.

Standard deviation is $8.6$ minutes.

Calculation:

In a $95\%$ confidence interval, $2.55$ of the area lies on each tail. The corresponding $z$ value is $1.960$ .

The formula to calculate the Maximum Error of Estimate is given by, $E=z\cdot \frac{s}{\sqrt{n}}$ .

Substitute $1.960$ for $z$ , $8.6$ for $s$ and $300$ for $n$ in the above formula.

  $\begin{array}{c}E=1.960\cdot \frac{8.6}{\sqrt{300}}\\ \approx 0.97\end{array}$

Therefore, the maximum error of estimate for the time spent in the gym using $95\%$ confidence interval is $0.97$ .

Therefore, the correct choice is G.