A Gallup poll from September 2014 stated that "sixty-one percent of Americans support allowing daily prayer to be spoken in the classroom..., down slightly from 66% in 2001." They report that 61% of the sample polled in 2014 supported allowing daily prayer to be spoken in the classroom, where as 66% of the sample polled in 2001 supported allowing daily prayer to be spoken in the classroom. The sample size for the 2014 poll was 1032. Assume the sample size for the 2001 poll was only 500.
(a) Calculate an approximate 95% confidence interval for the percent of all Americans that supported allowing daily prayer to be spoken in the classroom at the time of the 2001 survey.
(b) Calculate an approximate 95% confidence interval for the percent of all Americans that supported allowing daily prayer to be spoken in the classroom at the time of the 2014 survey.
(c) Is Gallup's statement that the percent of all Americans that support allowing daily prayer to be spoken in the classroom decreased from 2001 to 2014 justified? Explain.