In a survey conducted by the Gallup organization September 6-9, 2012, 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?" Of the 1,017
respondents, 214 said they had "no confidence at all."
a). Test, at the 5% level, if this sample provides evidence that the proportion of U. S. adults who have no confidence in the media differs significantly from 25%. Verify that the sample size is large enough to use the normal distribution to compute the p-value for this test and include all of the details of the test.(Please show work for all)

b). Verify that the sample size is large enough to use the normal distribution to construct a confidence interval for the proportion of U. S. adults who have no confidence in the media.

c). Construct a 90% 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.

Bonus:
d). What sample size is needed to reduce the margin of error to 1%?