Question

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

Short answer

The required correct option is$\left(b\right)$

Step-by-step solution

Given information

The proportion of people that jog regularly $\left(\hat{p}\right)=18\%=0.18$

Number of people $\left(n\right)=1600$

Margin of error$\left(E\right)=3\%=0.03$

The objective is to draw the calculation using the provided information

The formula for calculating the confidence interval for a population proportion is as follows:

$\hat{p}\pm E$

The confidence interval can be computed as follows:
$$\begin{gathered} CI=\hat{p}\pm E \\ =0.18\pm 0.03 \\ =(0.15,0.21) \end{gathered}$$

Using the above calculations, the true population proportion of people who jog could be estimated to be between$15\%$and$21\%$.

Therefore, the correct option is$\left(b\right)$