1. The Gallup Confidence in Institutions Survey The findings below, from a June 1-July 5 2021 poll, are the latest in Gallup's tracking of the public's confidence in a variety of key U.S. institutions, which began in 1973 during the Watergate scandal. Gallup has tracked 14 core institutions since 1993, and the public's confidence in them has remained relatively low - particularly over the past 15 years, when the average has not risen above 36%. Before 2006, averages at or above 40% were more common. In addition to the core institutions, Gallup measures confidence in other societal institutions, though with less frequency. Gallup interviews 500 US adults for each survey. Gallup uses random dial phone surveys to call adults within the United States, with approximately 40% landline and 60% cell phone respondents. Americans' Confidence in U.S. Institutions How much confidence do you, yourself, have in each one a great deat, quite a lot, some or very little? Great deal Quite a lo Some Smal business 30% The military 37% The police 20% The medical system 20% The presidency 16% The church or organized religion 19% The US Supreme Court 13% Banks 12% The public schools 13% Large technology comparses 12% 22% 10% 24% 17% 18% 25% 30% 32% 30% 34% 29% 42% 42% 39% 33% 24% 29% 26% 20% 30% 21% 9% c. The description of Gallup's polling methodology reports: "one can say with 95% confidence that the margin of error is 14 percentage points." Check the validity of this statement by calculating the estimated standard error using n = 500 and p = 0.37. Then, multiply the standard error by 2 to find the 95% confidence margin of error. How does your value compare to Gallup's margin of error? d. In June-July 2021, only 37% -0.37 of those surveyed reported a great deal or quite a lot of confidence in the church or organized religion. Find the 95% confidence interval for the sample distribution. Include a sentence to interpret the meaning. e. Does the 95% confidence interval indicate that in June-July 2021 it was likely that half of Americans have confidence in the church or organized religion? Explain your reasoning. f. In June-July 2021, 70%-0.70 of those surveyed reported a great deal or quite a lot of confidence in small businesses. Using the fact that the survey had a sample size n = 500 Americans, calculate the estimated standard error for those reporting a great deal or quite a lot of confidence in small businesses.