Q.1 - The Practice of Statistics for AP

Question

 The Gallup Poll interviews $1600$ people. Of these, $18\%$ say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a $95\%$ confidence level." You can safely conclude that

(a)  $95\%$of all Gallup Poll samples like this one give answers within$\pm 3\%$ of the true population value.

(b) the percent of the population who jog is certain to be between $15\% and 21\%$.

(c) $95\%$ of the population jog between$5\% and 21\%$ of the time.

(d) we can be $95\%$ confident that the sample proportion is captured by the confidence interval.

(e) if Gallup took many samples,$95\%$ of them would find that $18\%$ of the people in the sample jog.

Step-by-Step Solution

Answer

(a)  $95\%$of all Gallup Poll samples like this one give answers within$\pm 3\%$ of the true population value. 

Step-1 Given Information

Given in the question that,

Number of people$\left(n\right)=1600$

Margin of  error$=\pm 3\%$

sample proportion$=18\%$ we have to find the correct option.

Step-2 Explanation

The margin of error is expected to remain identical for all the confidence intervals because the size of the sample is identical and there would be $95\%$ of the samples that are expected to contain the true value of the population.

Hence, the correct option is (a).