A Gallup Poll asked 1022 randomly chosen adults whether the failure of the government to solve major challenges facing the country was a "crisis," a "major problem," a "minor problem," or "not a problem." The proportion giving the response "a minor problem" was 14 percent. The margin of sampling error was plus or minus 3 percentage points. Assume a 95 percent confidence level and no bias. From the information given above, one can make which of the following statements? (Note that 14 percent ± 3 percent is 11 percent to 17 percent.)
A) Between 11 percent and 17 percent of the sample responded, "a minor problem."
B) Between 11 percent and 17 percent of all American adults would respond, "a minor problem."
C) There is a 95 percent confidence (but not certainty) that between 11 percent and 17 percent of the sample responded, "a minor problem."
D) There is a 95 percent confidence (but not certainty) that between 11 percent and 17 percent of all American adults would respond, "a minor problem."

Question

Quizplus · Accepted Answer

Since the margin of error is plus or minus 3 percentage points, we can create a confidence interval of 14 percent plus or minus 3 percent, which gives a range of 11 percent to 17 percent. With a 95 percent confidence level, we can say that there is a 95 percent chance that the true proportion of all American adults who would respond "a minor problem" falls within this range. Therefore, option D is the correct choice. Option A is only applicable to the sample, not to the entire population. Option B is too broad of a statement since we cannot generalize our results to the entire population with certainty. Option C is incorrect because it only refers to the sample, not the entire population.

A Gallup Poll Asked 1022 Randomly Chosen Adults Whether the Failure