Q. 49 - The Practice of Statistics for AP

Question

49. A Gallup Poll found that only $28\%$ of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was $\pm 3$ 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’s 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

Step-by-Step Solution

Answer

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 1: Given information

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

Step 2: 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).