Use the following to answer the questions below:
In a survey conducted by the Gallup organization, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all."
-Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.
A) 0.184 to 0.236
B) 0.197 to 0.223
C) 0.394 to 0.446
D) 0.407 to 0.433

Question

Quizplus · Accepted Answer

The proportion of adults with no confidence is 214/1017 = 0.210. The standard error is sqrt[(0.210)(0.790)/1017] ≈ 0.013. The margin of error for a 95% confidence interval is 1.96 * 0.013 ≈ 0.025. Thus, the interval is 0.210 ± 0.025, or 0.185 to 0.235, which rounds to 0.184 to 0.236.

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