Question

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of $1600$ adults, the variation due to sampling error is no more than $3$

percentage points either way. The error margin is said to be valid at the $95\%$

confidence level. This means that, if the same questions were repeated in $20$ polls, the results of at least $19$ surveys would be within $3$ percentage points of the results of this survey.

Short answer

The results do not need to be in same margin of results. "At least" expression is wrong,

Step-by-step solution

Given Information

It is given that:

For a poll of $1600$ adults, the variation due to sampling error is no more than $3$

percentage points either way. The error margin is said to be valid at the $95\%$

confidence level. This means that, if the same questions were repeated in $20$polls, the results of at least $19$surveys would be within $3$percentage points of the results of this survey.

Explanation

The results of $19$among does not need to be in margin of results as it can give results which are not accurate for entire population.

It would have been correct to interpret that $19/20$has confidence intervals that contain true population proportion.

Also it is possible that less than $19$surveys have true population, it means "at least" is also incorrect.