Question

Losing weight A Gallup Poll found that 59% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For

results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 􀁯3 percentage points.”16 Can we use this interval to conclude that the actual proportion of U.S. adults who would say they want to lose weight differs from 0.55? Justify your answer.

Short answer

No, can not be concluded as 0.55 does not lie within the confidence.

Step-by-step solution

Step 1. Calculate the confidence interval.

It is given that the proportion of people who would like to lose weight is equal to 0.59. The margin of error is equal to $\pm 3$. The confidence interval is given as follows:

$\begin{array}{rcl}CI& =& \left(0.59-3,0.59+3\right)\\ & =& \left(0.56,0.62\right)\end{array}$

Step 2. Interpretation.

It can be observed that 0.55 does not lie within the confidence interval representing insufficient evidence to conclude that the actual proportion of US adults who will lose weight differs from 0.55.