Q. 49 49. A Gallup Poll found that onl... [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 8: Q. 49 (page 498)

49. A Gallup Poll found that only $28 %$ of American adults expect to inherit money or valuable possessions from a relative. The poll鈥檚 margin of error was $卤 3$ percentage points at a $95 %$ confidence level. This means that
(a) the poll used a method that gets an answer within $3 %$ of the truth about the population $95 %$ of the time.
(b) the percent of all adults who expect an inheritance is between $25 %$ and $31 %$ .
(c) if Gallup takes another poll on this issue, the results of the second poll will lie between $25 %$ and $31 %$ .
(d) there鈥檚 a $95 %$ chance that the percent of all adults who expect an inheritance is between $25 %$ and $31 %$ .
(e) Gallup can be $95 %$ confident that between $25 %$ and $31 %$ of the sample expect an inheritance

Short Answer

Expert verified

The option (a) is correct.

(a) the poll used a method that gets an answer within $3 %$ of the truth about the population $95 %$ of the time.

Step by step solution

Given information

The poll鈥檚 margin of error was $卤 3$ percentage points at a $95 %$ confidence level. To determine the correct option from the given statement.

Explanation

(a) The confidence level technique indicates that the true population proportion is within $3 %$ points of the sample mean.
As a result, the statement is correct.
(b) Only a $95 %$ confidence level can guarantee that the population percentage is between $25$ and $31$ .
As a result, the statement is false.
(c) Confidence intervals fluctuate depending on the sample.
As a result, the statement is false.
(d) Either $0$ or $1$ is the probability. Since the population percentage is between $25$ and $31$ percent at the $95 %$ confidence level.
As a result, the statement is false.
(e) The sample has a confidence level of $100 %$ that expects an inheritance between $25$ and $31$ percent .
As a result, the statement is false.
As a result, the right option is (a).