Chapter 8, Problem 104SE

To determine

Choose the option that reveals the meaning of the phrase ±4%.

Answer to Problem 104SE

The correct answer is “It would be unlikely to get the observed sample proportion of 0.73 unless the actual proportion of cell phone users who want e-mail service is between 0.69 and 0.77”.

Explanation of Solution

Margin of error:

In a confidence interval, the margin of error (E) denotes the range of values below and above the sample statistic. It represents the percentage points that the result could differ from the true population value.

Here, the margin of error is 4%. The confidence interval for the given scenario is as follows:

$\begin{array}{c}\text{Confidence interval}=\text{Sample statistic}\pm \text{Margin of error}\\ \text{=}0.73\pm 0.04\\ =\left(0.69,0.77\right)\end{array}$

According to the definition of margin of error, it represents that the actual proportion of cell phone users who want e-mail service is between 0.69 and 0.77.

From the given options, option d conveys the correct meaning for the margin of error.

The correct answer is “It would be unlikely to get the observed sample proportion of 0.73 unless the actual proportion of cell phone users who want e-mail service is between 0.69 and 0.77”.