54 Losing weight A Gallup Poll foun... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 9: 54 (page 564)

Losing weight A Gallup Poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or
results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 魛伅3 percentage points.鈥�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

Expert verified

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 $卤 3$ . The confidence interval is given as follows:

$\begin{array}{rcl} C I & = & (0.59 鈭� 3, 0.59 + 3) \\ = & (0.56, 0.62) \end{array}$

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.