Math: Question from KAPLAN (statistics)

[Kaushik]

Homework Statement

In a survey of 1,600 adults in the United States, 48% indicated that television is their primary source of news. The margin of error for the survey is ±2.5%. Which value is outside the interval that is likely to contain the exact percent of all adults in the United States who get the news primarily from television?

A. 45

B. 47

C. 49

D. 50

Relevant Equations

N/A

What exactly is the problem statement? what are they asking us to find?

 

[scottdave]

This article explains Margin of Error. https://www.statisticshowto.datasci...tatistics/hypothesis-testing/margin-of-error/

 

[Mark44]

Homework Statement:: In a survey of 1,600 adults in the United States, 48% indicated that television is their primary source of news. The margin of error for the survey is ±2.5%. Which value is outside the interval that is likely to contain the exact percent of all adults in the United States who get the news primarily from television?
A. 45
B. 47
C. 49
D. 50

What exactly is the problem statement? what are they asking us to find?

You gave the problem statement. They are asking you to find a number that isn't within the margin of error. For example, if a length is measured as 130 cm, with a margin of error of 5cm, it means that the true length is somewhere between 125 cm. and 135 cm.

 

[scottdave]

Except they gave a percentage margin of error, so you need to calculate the range of credible answers, then see which of these is not in that range.

 

[Kaushik]

that is likely to contain the exact percent of all adults in the United States who get the news primarily from television?

What exactly does this (second part) mean?

ik that it is trivial, but I would love to understand it rather than 'ignoring' it.

 

[PeroK]

What exactly does this (second part) mean?

ik that it is trivial, but I would love to understand it rather than 'ignoring' it.

The assumption is that there is a well-defined percentage of adults in the US who get their news primarily from TV. This might be 1%, 10%, 50%, 99% or even 100%.

But, a survey is done that estimates that percentage as 48%, with a 2.5% margin of error. That narrows things down and rules out things like 1%, 10%, 99%.

Which of the percentages given (45, 47, 49, 50) is ruled out by the survey?

 

[hutchphd]

Let me flesh this out just a little. If they could survey everybody in the US then they could provide a certain answer to the question "what percentage ...".e.g. say 47.785%. But it is impractical to ask everyone so you ask what is hopefully a representative sample. The sample is never exactly representative but the bigger the sample the better. Through statistical methods it is possible to put bounds on how likely it is that your sample differs from the actual population. Hence the question statement.
These methods are extraordinarily powerful and useful in real world problems be it counting people or producing widgets. They are well worth comprehensive understanding.!

 

[haruspex]

Except they gave a percentage margin of error, so you need to calculate the range of credible answers, then see which of these is not in that range.

It is not made clear, but I think the given margin is as a number of percentage points, not a percentage of a percentage value.

 

[scottdave]

It is not made clear, but I think the given margin is as a number of percentage points, not a percentage of a percentage value.

I was wondering about that. Now that I think about it, the way you word it makes sense, in this situation.